At issue in this maritime-shipping dispute is whether the district court erred in determining liability and damages for cold-rolled steel coils and steel pipes shipped on the MEDI TRADER from Eastern Europe to Houston and New Orleans. Western Bulk challenges: the district court’s finding the coils were undamaged when loaded onto the MEDI TRADER, but damaged when unloaded; its damages assessment; and its finding Western Bulk was the sole Carriage of Goods by Sea Act (COGSA) carrier — and therefore the sole party liable for damages — with respect to TradeArbed, Inc. (the coils’ owner), and Freemak Industries, Inc. (the pipes’ owner). AFFIRMED.
I.
Western Bulk was the last in a chain of time charterers of the MEDI TRADER, tracing back to her owner, Seafarers Shipping, Inc. Seafarers was a party to this action, but, post-trial, was dismissed without prejudice, as discussed infra.
A.
The cargo at issue for TradeArbed and Freemak is described in turn. The primary disputes concern TradeArbed.
*4661.
In December 2002, TradeArbed entered into a charter party with Western Bulk to ship hot-rolled and cold-rolled steel coils on the MEDI TRADER, from Bourgas, Bulgaria, to New Orleans. TradeArbed later became Arcelor Trading (they are referred to as TradeArbed). (Although it does not affect this analysis, there were two charter parties signed on 5 December 2002. Western Bulk negotiated one with TradeArbed; the other, with Arcelor Trading. The latter exists to reflect the above-noted merger. The charter parties refer only to “Hot Rolled Coils”, but the parties understood this term covered cold-rolled coils as well.)
TradeArbed’s coils were loaded onto the MEDI TRADER in January 2003. The moisture-sensitive cold-rolled coils were shipped in the usual protective wrappings; the non-moisture-sensitive hot-rolled coils were not wrapped. TradeArbed’s damages at issue concern only the cold-rolled coils.
Three bills of lading (numbers six-eight) covered the cold-rolled coils, and each noted tears, dents, and minor rust on some of the wrappings. Otherwise, the bills were clean.
TradeArbed’s coils were stowed in holds one, three, and five. After loading in Bourgas, hold one contained cold-rolled coils covered by bill six, along with Tra-deArbed’s bill-nine cold-rolled coils and another shipper’s galvanized-rolled coils (also moisture-sensitive, the galvanized-rolled coils were wrapped similar to cold-rolled coils); hold three contained cold-rolled coils covered by bill seven, along with some of TradeArbed’s hot-rolled coils and another shipper’s galvanized-rolled coils; and hold five contained cold-rolled coils covered by bills seven and eight, along with more of TradeArbed’s hot-rolled coils.
Holds two and four were filled with other shippers’ cargo. Cargo was added to holds one and three at a subsequent port, before ocean transit to the United States.
Evidence was presented at trial regarding the existence of condensation in the holds, which can cause rust on moisture-sensitive cold-rolled coils. The moisture was claimed to have entered the holds from either or both of two principal sources.
First, it could have entered with non-moisture-sensitive cargo, like the hot-rolled coils, which, prior to loading, were stored in the open air and were covered with snow during loading. During loading, the MEDI TRADER’S chief mate objected to stowing wet hot-rolled coils in the same hold with moisture-sensitive cold-rolled coils.
Second, moisture could have entered when, at a subsequent port, cargo was loaded into the holds during rainfall. This was also over the chief mate’s protests.
After discharging some of her cargo in Houston, including Freemak’s pipes, the MEDI TRADER proceeded to New Orleans, where her remaining cargo, including the cold-rolled coils, was unloaded; those coils were still in wrappers. In both Houston and New Orleans, a number of surveyors inspected the cargo and the holds.
Surveyors agreed hold three contained “tide marks” — evidence of standing water in the hold. In the three holds containing the coils at issue, surveyors also found “drip-down condensation” resulting from water condensing at the top of the hold and dripping onto the cargo. Surveyors generally agreed this was fresh-water, as opposed to salt-water, condensation, and attributed it to the moisture introduced during loading. It was also noted that some coils were dripping water during unloading in New Orleans.
*467TradeArbed’s cold-rolled coils were loaded from the MEDI TRADER onto barges for shipment to their final destinations up the Mississippi River. They were not unwrapped until they reached those destinations.
The original buyer of the bills-seven and -eight coils rejected them as unfit, citing heavy rust. Another round of surveys generally attributed the rust to moisture encountered in ocean transit. Tra-deArbed sold those coils to the original buyer at a depreciated value. Surveys approved of the new sale price as “fair, reasonable, [and] representative of] conditions viewed”.
The bill-six coils were rejected based on damage caused by rust and oil emulsification within the coils. More so than with the bills-seven and -eight coils, evidence conflicted on whether the bill-six coils were damaged in ocean transit. The original buyer of those coils rejected them, but TradeArbed reached agreement with a different buyer to purchase them at a depreciated value. Surveys described the new bill-six sale price as “representat[ative of] conditions viewed, ... fair, reasonable, and ... recommended as the best disposition in the matter....”
2.
For the same voyage on the MEDI TRADER, Freemak also chartered, from Western Bulk, space to ship its steel pipes. They were loaded in December 2002 in Odessa, Ukraine. Upon unloading them in Houston, it was discovered they had been crushed by rebar. As it did at trial, Western Bulk concedes the pipes were damaged during the ocean transit.
B.
TradeArbed and Freemak filed an action for damages against: the MEDI TRADER, in rem; her owner (Seafarers); her manager (Victoria Ship Management, Inc.); and her charterer (Western Bulk). The district court consolidated the action with one filed earlier by Cargill Ferrous International, another shipper with cargo on the MEDI TRADER during the voyage at issue. Seafarers and Victoria filed a cross claim and a third-party complaint against Western Bulk, seeking indemnification for damage to the cargo.
The district court bifurcated the trial, separating “the cargo quantum claims from the issues of liability between [Western Bulk] and Seafarers”. Cargill Ferrous Int'l v. M/V MEDI TRADER, 513 F.Supp.2d 609, 612 (E.D.La.2007). The second part of the bifurcated trial has yet to occur.
After a bench trial on the claimed cargo damage, the district court found Western Bulk liable, inter alia, to TradeArbed for $787,222.44 for the bill-six through bill-eight coils; and, to Freemak for $256,814.22 for the pipes. MEDI TRADER, 513 F.Supp.2d at 625-26. (A significant portion of the district court’s opinion was devoted to Cargill’s claims, and Cargill was awarded damages of, inter alia, $264,452.67. Cargill settled its claims.) Western Bulk’s motions for reconsideration and for a new trial were denied.
On 20 October 2008, an omnibus order: dismissed without prejudice claims that settled after trial (not at issue in this appeal); and, consistent with its earlier opinion, awarded judgment for Tra-deArbed and Freemak against Western Bulk.
II.
For this admiralty bench trial, the district court heard no testimony; only documentary evidence was presented. The court’s legal conclusions are reviewed de novo; its findings of fact, only for clear error. E.g., Sabah Shipyard Sdn. Bhd. v. M/V HARBEL TAPPER, 178 F.3d 400, *468404 (5th Cir.1999) (citing Nerco Oil & Gas, Inc. v. Otto Candies, Inc., 74 F.3d 667, 668 (5th Cir.1996)). Benchtrial fact findings, “whether based on oral or other evidence, must not be set aside unless clearly erroneous .... ” Fed R. Civ. P. 52(a)(6). Restated, this standard is applied even though the district court made no credibility determinations based on oral testimony and based them only on “documentary evidence or inferences from other facts”. Pacific Employers Ins. Co. v. M/V GLORIA, 767 F.2d 229, 235 (5th Cir.1985) (quoting Anderson v. City of Bessemer City, North Carolina, 470 U.S. 564, 574, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985)).
Western Bulk contends: TradeArbed failed to prove its prima facie case for damage to cargo; the district court applied an improper method to calculate damages and, in the alternative, erred by not applying COGSA’s $500-per-package damage limitation; and this was an instance of common, not private, carriage, and, consequently, Western Bulk is not the only party liable as a COGSA carrier.
A.
Regarding the claimed cargo damage, Western Bulk contends TradeArbed failed to prove two essential elements of its COGSA prima facie case: Western Bulk’s receipt of the cargo in good condition; and its delivery in damaged condition. See Tubacex, Inc. v. M/V RISAN, 45 F.3d 951, 954 (5th Cir.1995). Each element is addressed in turn.
1.
Regarding good condition on receipt, Western Bulk asserts: the coils did not have clean bills of lading; and TradeArbed failed, in the absence of such bills, to prove good condition by other means. In that regard, Western Bulk contends Tra-deArbed failed to offer any proof of the coils’ condition on receipt because it failed to show their condition inside their wrappings.
Clean bills of lading are prima facie evidence of good condition on receipt. Steel Coils, Inc. v. M/V LAKE MARION, 331 F.3d 422, 426 (5th Cir.2003). As noted, the bills were not entirely clean. MEDI TRADER, 513 F.Supp.2d at 625-26. In such a situation, the district court must look to other evidence to determine good condition, such as mate’s receipts and surveys from the loading port. See LAKE MARION, 331 F.3d at 427.
As noted, Western Bulk contends Tra-deArbed failed to meet a “considerable burden of going further to prove actual condition”, because it did not present evidence of the coils’ condition inside their wrappings. See United States v. Lykes Bros. Steamship Co., 511 F.2d 218, 223 (5th Cir.1975) (quoting Compagnie De Navigation v. Mondial United Corp., 316 F.2d 163, 170 (5th Cir.1963)); see also Caemint Food, Inc. v. Brasileiro, 647 F.2d 347, 352 (2d Cir.1981). Our court has, however, expressly distinguished the “considerable burden” placed on shippers of the wrapped perishable goods in Western Bulk’s cited cases from the burden placed on shippers of wrapped steel coils. See LAKE MARION, 331 F.3d at 429.
In LAKE MARION, the owner of cold-rolled steel coils sued for damages allegedly incurred during maritime transit. Id. at 425. After a bench trial, the district court awarded damages. Id.
As Western Bulk does here, in LAKE MARION it was contended on appeal: “the bill of lading notation that the condition of these coils was unknown fatally undermined Steel Coils’s attempt to prove a prima facie case of good condition” at loading. Id. at 428. Our court disagreed, holding:
The evidence at trial shows that, had the cold rolled ... coils been damaged by *469rust, their outer -wrappers would have revealed it. Because the wrappers had no indication of rust, and the moisture on the outside of the wrappers was not dripping down into the coils, it was not clearly erroneous for the district court to conclude that the cold rolled ... coils were in an undamaged state prior to loading.
Id. at 429; see also Couthino, Caro & Co. v. M/V SAVA 849 F.2d 166, 168 (5th Cir.1988) (affirming district court’s finding, based on witness’ testimony, that steel coils were undamaged at loading despite “numerous exceptions noting rust and packaging damage” on bills of lading).
In the instant action, the district court relied on the pre-load surveys and other evidence introduced at trial to find whether the cargo was in good condition at loading. The court ruled: “while the bills of lading were claused to note some defects in packaging and the load survey also demonstrates this, it is the Court’s conclusion after viewing the photographs that[, at loading,] any rust on the coils themselves was on the hot rolled coils”, not the cold-rolled coils. MEDI TRADER, 513 F.Supp.2d at 626. Therefore, for the cold-rolled coils, the district court found Tra-deArbed proved the undamaged-at-loading element of its prima facie case. Id.
TradeArbed was not required to do more. See LAKE MARION, 331 F.3d at 429. The district court did not clearly err in finding the cold-rolled coils’ undamaged condition at loading. See GLORIA, 767 F.2d at 235 (stating that, “ ‘[w]here there are two permissible views of the evidence, the factfinder’s choice between them cannot be clearly erroneous' ... even when the district court’s findings do not rest on credibility determinations, but are based instead on physical or documentary evidence or inferences from other facts’ ” (quoting Anderson, 470 U.S. at 574, 105 S.Ct. 1504)).
2.
Likewise, Western Bulk asserts Tra-deArbed failed to prove the coils were damaged on delivery, maintaining it failed to present any evidence of the coils’ condition because they were not unwrapped in New Orleans, but remained packaged until they reached their upriver destinations. According to Western Bulk, the light atmospheric rust on the coils’ wrappings at discharge in New Orleans does not explain the heavier fresh-water rust discovered on the coils when unwrapped over a month later. Western Bulk also suggests the coils could have been damaged in storage after reaching those destinations.
In LAKE MARION, as here, it was contended: “the steel coils rusted on the way from the ship to their ultimate inland destinations”. 331 F.3d at 429. LAKE MARION ruled such contentions were “belied by a wealth of evidence relied upon by the district court”, including a quoted survey that stated the surveyor’s opinion as to the cause of the damage. Id. Accordingly, this issue turns on whether evidence in the record precludes holding clearly erroneous the finding that the coils were damaged in ocean transit.
The district court considered two separate. groups of coils, and held: “Tra-deArbed/Arcelor has carried its burden of proof to demonstrate that the [bills-seven and -eight] coils were unloaded in a damaged condition as they were rusted”, and the bill-six coils were “also damaged as a result of incompatible cargo being stowed together”. MEDI TRADER, 513 F.Supp.2d at 626.
a.
Regarding the bills-seven and -eight coils, Western Bulk maintains the district court improperly relied on six surveys— three in New Orleans, and three at the upriver destinations — cited to support its *470finding that those coils were rusted during ocean carriage. Western Bulk contends: the upriver surveys do not prove damage at unloading in New Orleans; and the earlier New Orleans surveys do not show rust on the coils because they were not unwrapped.
For the coils shipped in hold three, surveys reported “rust tide mark” and “heavy drip down”, resulting from “ship’s sweat and cargo sweat in the cargo hold due to the lack of proper ventilation and from faulty stowage”. One New Orleans surveyor, inspecting the three holds that contained TradeArbed’s coils, concluded: “the heavier rust to various degrees noted on the cargo in each hold was due to sweat ... caused as a result of improper ventilation aboard the ocean carrier [and] improper stowage aboard the ocean carrier”. The coils were found to have been subject to “severe sweat conditions prior to loading the barges” for the upriver journey. As one survey explained: “Stowage of hot rolled steel cargo in the same cargo compartment as moisture sensitive cargo is improper stowage. Ventilation of the cargo was impeded and therefore improper....”
These surveys support the district court’s finding that the bills-seven and - eight coils were damaged when unloaded in New Orleans; therefore, the court did not clearly err when it credited them.
b.
As noted, after the bill-six coils’ original buyer rejected them, TradeArbed reached an agreement with another buyer to sell those coils at a discount based on “rust/oil emulsification only”. The district court found these coils were “primarily damaged by oil emulsification” resulting from “a combination of oil and water from the high humidity in the cargo holds”. MEDI TRADER, 513 F.Supp.2d at 626. As also noted, the district court attributed this damage to “incompatible cargo being stowed together”. Id.
Surveys conflicted as to the bill-six coils’ conditions, and opinions conflicted on the cause of damage. Evidence showed moisture in hold one. A number of the bill-six coils’ wrappings were torn, punctured, or otherwise damaged, thereby creating holes through which this moisture could reach the coils and cause emulsification and rust. “[M]oderate/heavy oxidation/rust” on the bill-six coils was found at discharge in New Orleans.
In short, some evidence suggested the damage did not occur during ocean transit. Nevertheless, the district court did not clearly err when it credited contrary evidence and found the bill-six coils were damaged at unloading.
B.
Accordingly, the district court did not clearly err when it found TradeArbed proved its COGSA prima facie case that the goods were damaged during ocean transit. Therefore, the contested damages are addressed next. In challenging the district court’s method of calculating them, Western Bulk presents two alternative claims: TradeArbed failed to satisfy its initial burden to prove a prima facie case of damages; and, in the alternative, the court erred by denying Western Bulk the benefit of COGSA’s $500-per-package damage limitation.
1.
Western Bulk contends: because Tra-deArbed failed to prove the coils’ sound market value at discharge in New Orleans, in both their damaged and undamaged states, the district court should have denied all recovery. Using the coils’ subsequent upriver value to determine damages, Western Bulk asserts, is contrary to our *471precedent requiring damages to be calculated using market value at discharge.
As for the cargo covered by bills-seven and -eight, the district court stated only that “the damages suffered were $574,542.83”, and cited a survey describing that this amount was calculated by subtracting the discounted price for the damaged coils from the original price. MEDI TRADER, 513 F.Supp.2d at 626. The distinct court resolved the bill-six coils’ damages similarly, finding “damages [were] $212,679.61 after mitigation of damages by TradeArbed/Arcelor through acceptance [of] reasonable depreciation”, and cited a survey providing the relevant calculation. Id. These calculations were not improper under our precedent.
COGSA does not mandate one method of calculating damages, but instead provides a general principle: “In no event shall the carrier be liable for more than the amount of damage actually sustained”. COGSA, § 4(5), 46 U.S.C. § 30701 note. Our court typically applies the traditional “market value rule” to calculate COGSA damages. See BP N. Am. Petroleum v. SOLAR ST, 250 F.3d 307, 312 (5th Cir.2001). As the Supreme Court has recognized, however, there are occasions when it is necessary to use other methods. See Ill. Cent. R.R. Co. v. Crail, 281 U.S. 57, 64-65, 50 S.Ct. 180, 74 L.Ed. 699 (1930) (“The test of market value is at best but a convenient means of getting at the loss suffered. It may be discarded and other more accurate means resorted to, if, for special reasons, it is not exact or otherwise not applicable.”).
In F.J. Walker Ltd. v. M/V LEMON-CORE our court held: where the carrier is responsible for damages, it “is in no position to complain that the damaged parties can not establish precisely the loss it caused”. 561 F.2d 1138, 1147 (5th Cir.1977) (citing Daniels Towing Svc., Inc. v. Nat Harrison Assoc., Inc., 432 F.2d 103, 105-06 (5th Cir.1970)). The LEMON-CORE district court “was faced with establishing damages by one of two methods, both of which were inexact”. Id. at 1147. After noting the “primary object in awarding damages is to indemnify plaintiff for the loss sustained by reason of the carrier’s fault”, LEMONCORE made clear that inability to prove exact damages is not fatal to a shipper’s case. See id. at 1146-47 (quoting Interstate Steel Corp. v. S.S. Crystal Gem, 317 F.Supp. 112, 121 (S.D.N.Y.1970)) (holding that where damages are unclear or difficult to prove, “the court should use the best indication it can obtain rather than deny any recovery”).
Restated, uncertainty does not preclude recovery. Id; see also Saul Sorkin, Goods in TRANSIT § 11.03 n. 27 (2009) (“Uncertainty in ascertaining damages does not mean that plaintiff is precluded from i’e-eovering.” (citing C. Itoh & Co. v. Hellenic Lines, Ltd., 470 F.Supp. 594, 598 (S.D.N.Y.1979))). “In such a situation the district court has a discretion to choose the method it considers best.” LEMONCORE, 561 F.2d at 1147 (citing Ill. Cent., 281 U.S. 57, 50 S.Ct. 180; Santiago v. Sea-Land Svc., Inc., 366 F.Supp. 1309, 1314-15 (D.P.R.1973)).
LEMONCORE ultimately approved a method of calculating damages similar to the market-value method urged by Western Bulk; but, in this instance, it is the general COGSA-damages principles LEM-ONCORE expresses that are persuasive. In the light of such principles, the district court did not err by not requiring at-discharge market value. Obviously, because of the nature of transporting cold-rolled coils, TradeArbed could not discover the extent of the damage to them until they were unwrapped; and, because their ultimate destinations were upriver, they were not unwrapped until more than a month after they were discharged from *472the MEDI TRADER (and thereby discharged from Western Bulk’s control).
TradeArbed’s evidence regarding bills-seven and -eight cargo included: invoices (which can be used to determine market value, see Emmco Ins. Co. v. Wallenius Caribbean Line, S.A., 492 F.2d 508, 514 (5th Cir.1974)) and sale confirmations for the coils corresponding with sale contracts entered both before and after discharge (both for the same price, $18.83 cwt); evidence of the price for which the coils were sold at salvage ($11.80 cwt); and an expert opinion that the salvage price was “fair, reasonable, [and] represents conditions” of the damaged coils as viewed during the survey. The evidence regarding the bill-six coils was similar, with a contract price of $21 cwt and a salvage price of $11.60 cwt.
The salvage-sale agreements, which Tra-deArbed entered after its original buyers complained that the coils were damaged, were necessarily non-existent at discharge because TradeArbed did not know, and could not have known, of the damage, or its extent, at that time. These agreements contemplated the percentages of coils damaged and were otherwise specific to the status of each set of coils. TradeArbed could not have produced evidence of the at-discharge “market price” of this certain number of coils containing this certain number of various defects. Western Bulk provides no reason to find clearly erroneous the district court’s finding TradeArbed presented sufficient evidence to determine actual damages.
Western Bulk relies on SOLAR ST, which concerns damages for oil sold at a discount after being negligently contaminated by its carrier. That case, however, is distinct in several ways from the instant matter. For example, unlike the SOLAR ST district court, see 250 F.3d at 315, the district court here was not presented with evidence it could have used to apply the market value rule. As another example, the district court’s damage determination in this instance did not implicate concerns that using a subsequent value would make the carrier a “guarantor of the ups and downs of commodity prices”. See Holden v. SS KENDALL FISH, 395 F.2d 910, 913 (5th Cir.1968); see also SOLAR ST, 250 F.3d at 312-15. As a final example, for the bills-seven and -eight coils, evidence showed the market relevant to this transaction — ie., the value of the undamaged goods vis-a-vis TradeArbed and the buyers — did not fluctuate between discharge and re-sale.
2.
For its alternative damages contention — that the district court should have applied COGSA’s $500-per-paekage limitation — Western Bulk maintains: either the charter party is the contract of carriage, and COGSA is thereby incorporated; or, the bills of lading are the contracts of carriage, and COGSA applies of its own force. The COGSA package limitation provides, in relevant part:
Neither the carrier nor the ship shall in any event be or become liable for any loss or damage to or in connection with the transportation of goods in an amount exceeding $500 per package ... unless the nature and value of such goods have been declared by the shipper before shipment and inserted in the bill of lading. This declaration, if embodied in the bill of lading, shall be prima facie evidence, but shall not be conclusive on the carrier.
By agreement between the carrier, master, or agent of the carrier, and the shipper another maximum amount than that mentioned in this paragraph may be fixed: Provided, That such maximum shall not be less than the figure above named. In no event shall the carrier be *473liable for more than the amount of damage actually sustained.
46 U.S.C. § 30701, note § 4(5).
Western Bulk asserts the charter party it negotiated with TradeArbed required that COGSA be incorporated in all bills of lading, and suggests this gave the requisite notice and opportunity for TradeArbed to declare a higher value. See generally Brown & Root, Inc. v. M/V PEISANDER, 648 F.2d 415, 420-25 (5th Cir.1981) (discussing fair-opportunity doctrine). Further, Western Bulk contends TradeArbed, a sophisticated shipper, is not the type party the fair-opportunity doctrine is designed to protect.
The district court held: “COGSA, with the exception of the limit of recovery, applies to these contracts of carriage”, ruling that “neither [the charter parties] nor the bills of lading evidence a fair opportunity to declare a higher value for the shipment so as to invoke the ... package limitation because mere incorporation of [COGSA] into the bills of lading through the charter party is insufficient notice”. MEDI TRADER, 513 F.Supp.2d at 625.
Contrary to Western Bulk’s position, to invoke the package limitation, it is necessary to provide further evidence beyond incorporation of COGSA into the contract of carriage, such as the carrier’s giving the shipper a choice of rates and valuations. See SAVA, 849 F.2d at 171 n. 6 (“[W]e have not held ... that the mere incorporation of COGSA into a bill of lading constitutes prima facie evidence of fair opportunity”.). The carrier bears an initial burden of showing it offered the shipper a fair opportunity to avoid the limitation. Id. at 169. A prima facie case of fair opportunity can be made by introducing, e.g., evidence of a published tariff that “very carefully gave Shipper a choice of valuations by a choice of precisely definable freight rates”. PEISANDER, 648 F.2d at 424; see also Wuerttembergische & Badische Versicherungs-Aktiengesellschaft v. M/V STUTTGART EXPRESS, 711 F.2d 621, 622 (5th Cir.1983) (applying PEISANDER to invoke COGSA package limitation and emphasizing existence of tariff that “clearly gave the shipper a choice of valuations”).
The district court did not clearly err in finding: that Western Bulk did not provide TradeArbed sufficient notice of a fair opportunity to declare a higher value; and that, therefore, the package limitation did not apply.
C.
Finally, Western Bulk challenges the district court’s awarding damages before the second stage of the bifurcated trial. The award was based on the district court’s ruling Western Bulk was the only COGSA carrier of TradeArbed’s coils and Freemak’s pipes. Western Bulk contends: the district court should have treated its carriage of cargo on the MEDI TRADER as common, not private; and the bills of lading, not the charter parties, constituted the applicable contracts of carriage. If carriage were common, Seafarers (the MEDI TRADER’S owner) would also be a COGSA carrier liable for damage to the cargo.
1.
Charter parties are the contracts of carriage in private carriage, but bills of lading are such contracts in common carriage. See Thomas J. Sohoenbaum, Admiralty and Maritime Law § 11-6 (2004). The district court’s deciding Western Bulk was the sole COGSA carrier of the cold-rolled coils and, therefore, the only party liable for damages to them, flowed from its ruling the charter party, not the bills of lading, was the relevant contract of carriage between TradeArbed and Western Bulk. Western Bulk was the only charterer to sign this *474charter party, and our precedent “requires privity of contract of carriage before liability under COGSA arises”. Thyssen Steel Co. v. M/V KAVO YERAKAS, 50 F.3d 1349, 1353 (5th Cir.1995).
The issue turns, therefore, on whether the district court erred when it found the applicable contract of carriage to be the charter party, not the bills of lading (signed not only by Western Bulk, but also by an agent of Seafarers, the MEDI TRADER’S owner). See MEDI TRADER, 513 F.Supp.2d at 624-25. Western Bulk maintains the MEDI TRADER was engaged in common carriage because it carried more than one shipper’s cargo.
In Thyssen, Inc. v. NOBILITY MV, 421 F.3d 295 (5th Cir.2005), as here, the district court found a voyage charter, not the bills of lading, was the contract of carriage, id. at 304, where the ship also “carried other cargo ... on behalf of another cargo shipper”, id. at 297. As here, the bills of lading specifically incorporated the charter. Id. at 307. Reviewing for clear error, our court affirmed the district court’s finding the ship “was engaged in private carriage”, id., and denied the contention that “multiple shipping defeats any indication of private carriage that a bill of lading incorporating the terms of the voyage charter may connote”, id. at 305.
Pursuant to NOBILITY, the district court did not err in deciding the MEDI TRADER was engaged in private carriage with respect to TradeArbed’s coils, with the charter party, not the bills of lading, being the applicable contract of carriage. Therefore, Western Bulk, as the only charterer that signed the charter party, was the only party in privity with TradeArbed. Because, as noted, our precedent requires privity for COGSA carrier liability, Western Bulk was the only COG-SA carrier; no COGSA liability allocation remains to be resolved at the second stage of the bifurcated trial. Accordingly, the district court did not err in awarding damages against only Western Bulk for Tra-deArbed’s coils.
2.
Western Bulk also contends the district court erred because it did not reserve allocation of liability for damages to Free-mak’s pipes for the second part of the bifurcated trial, asserting the district court should have only determined the amount of damages. Western Bulk claims its failure to introduce evidence as to the cause of the pipes’ damages was in reliance on the bifurcation order separating “cargo quantum claims” from “issues of liability”.
This claim, as with the coils, turns on whether Western Bulk was the only COGSA carrier for the pipes. For the same reasons the charter party between Tra-deArbed and Western Bulk constitutes the contract of carriage between those parties, the district court ruled: “The private carriage agreement ... between Western Bulk and Freemak is the controlling contract of carriage” for the pipes. MEDI TRADER, 513 F.Supp.2d at 624.
As with the TradeArbed bills of lading, the Freemak bills expressly incorporated the relevant charter party. Nothing about the Freemak charter party suggests or compels a conclusion inconsistent with our earlier holding as to TradeArbed. For the reasons provided supra, the district court did not err in deciding the charter party, rather than the bills of lading, was the contract of carriage; and, in concluding Western Bulk was the sole carrier of Free-mak’s pipes.
Because the district court did not err in determining Western Bulk to be the sole carrier for the pipes, its awarding damages against Western Bulk is not inconsistent with the bifurcation order. As the sole COGSA carrier, Western Bulk is solely responsible for the COGSA damages. *475This result does not mean, as Western Bulk asserts, that the district court treated Western Bulk’s admission that the pipes were damaged as tantamount to an admission of liability. Rather, the court’s ruling that Western Bulk was the sole carrier simply precluded consideration of the further question of how to allocate liability among the carriers, which would have been considered at the second stage of the bifurcated trial.
III.
For the foregoing reasons, the judgment is AFFIRMED.