On August 31, 1985, plaintiff Bradier Steve Landol Rivera was working as night manager of the Golden Skillet fast-food restaurant in Guaynabo, Puerto Rico, when a robber entered, jumped over the counter and, at gunpoint, demanded all of the available cash. Landol managed to telephone the police, and several officers drove up to the restaurant while the robber was still inside. The suspect grabbed Landol and started to leave through the back door, where he confronted two officers, weapons *792drawn. The police yelled at the suspect that he was not going to get out; the suspect yelled back that, “[i]f you don’t let me get out, I’ll kill him.”
The robber returned inside and escaped through the front door, still holding plaintiff at gunpoint. He ran into the street and commandeered a passing car, taking over the driver’s position with Landol on his lap. When the car moved slightly, the pursuing officers fired. One bullet hit plaintiff in the jaw, severely injuring him. The robber was apprehended immediately thereafter, and Landol was taken to a hospital.
Based on this incident, Landol brought a damages suit under 42 U.S.C. § 1983, alleging that the police actions violated various constitutional provisions.1 A jury found that three officers violated his Fourth Amendment right to be free from an unreasonable seizure, and awarded him $105,000 in damages.2 Two of the officers assert on appeal several reasons why they may not be held liable:3 (1) plaintiff had no Fourth Amendment claim; (2) he failed to show which officer fired the shot that struck him, and thereby caused his injury; (3) the officers are entitled to qualified immunity. After carefully reviewing the record and the caselaw, we have concluded that the jury’s verdict was legally unsound. We therefore reverse the district court’s denial of defendants’ motion for judgment notwithstanding the verdict, and remand to that court so that it may enter judgment for defendants.
I.
A.
The Fourth Amendment to the United States Constitution protects individuals against “unreasonable searches and seizures.” Defendants argue that the primary issue before us is whether plaintiff’s shooting by a police officer may be termed a “seizure” that implicated the Fourth Amendment. They claim that the Fourth Amendment is inapplicable here because the police officers who fired their weapons were not attempting to restrain plaintiff’s freedom but were attempting only to apprehend the robber.
This is a compelling argument that, ordinarily, we would not consider because it was not raised below. “It is a fundamental principle that, except in rare cases where paramount considerations of justice require, we do not review on appeal issues that were not first presented to the district court.” Rodriguez Rodriguez v. Munoz Munoz, 808 F.2d 138, 140 (1st Cir.1986). This case strikes us as exceptional, however, because the question raised by defendants concerns the very premise of plaintiff’s claim for damages and because any perceived legitimation of that premise would be fraught with mischief. We therefore think it appropriate to consider it despite the technical default. “[W]e address the issue of whether any constitutional right of the plaintiff has been violated because of its central and essential character in this Section 1983 action.” Izquierdo Prieto v. Mercado Rosa, 894 F.2d 467, 471 n. 4 (1st Cir.1990) (emphasis in original) (considering sua sponte whether plaintiff had Equal Protection claim).
Moreover, our consideration of this issue will not “sandbag” the trial judge with a legal problem he had no reason to contemplate. In his decision on defendants’ motion for summary judgment, the district *793judge questioned whether the police officers’ actions here should be construed as a seizure under the Fourth Amendment in light of the unintentional nature of plaintiffs shooting. The court concluded that Fourth Amendment analysis was required based on a First Circuit case stating that “ ‘a law enforcement officer “seizes” someone by shooting him.’ ” Opinion and Order on Summary Judgment at 7 n. 3 (quoting Fernandez v. Leonard, 784 F.2d 1209, 1216-17 (1st Cir.1986)). As we explain below, this is a mistaken view of the law, and we think it worth clearing up the misunderstanding. Cf. Rodriguez Rodriguez, 808 F.2d at 140.4
We therefore now turn to the question of whether Landol was “seized” within the meaning of the Fourth Amendment.5
B.
In Tennessee v. Garner, 471 U.S. 1, 105 S.Ct. 1694, 85 L.Ed.2d 1 (1985), the Supreme Court considered whether the Fourth Amendment was violated when a police officer fatally shot an unarmed burglary suspect who was attempting to escape. In the course of deciding that shooting the suspect was constitutionally impermissible in the circumstances of that case, the Court observed that, “there can be no question that apprehension by the use of deadly force is a seizure subject to the reasonableness requirement of the Fourth Amendment.” Id. at 7, 105 S.Ct. at 1699. The Court held that deadly force is permissible only if it is necessary to prevent a suspect’s escape and if “the officer has probable cause to believe that the suspect poses a significant threat of déath or serious physical injury to the officer or others.” Id. at 3, 105 S.Ct. at 1697.
The district court in this case, in its response to defendants’ motion for summary judgment, relied on Garner in concluding that the use of deadly force against the fleeing robbery suspect was reasonable. We quote its well-stated explanation:
[Tjhere is no question of fact, whatsoever, as to whether the defendant police officers had probable cause to believe that the suspect posed a threat of serious physical harm to the officers or to others. ... At the time the police employed the alleged “deadly force,” they were aware of the following: that the suspect had committed armed robbery in a public restaurant and was fleeing from the police; that the suspect was keeping the plaintiff hostage at gunpoint and had threatened to kill plaintiff if he was not allowed to “get out;” that he had attempted to hijack a private vehicle at gunpoint; and that he had successfully hijacked a second vehicle and its driver at gunpoint, in a public traffic intersection. Such undisputed facts would clearly constitute probable cause sufficient to justify an officer’s use of deadly force against the fleeing suspect in this case.
Opinion and Order on Motion for Summary Judgment, at 5-6 (emphasis deleted). We think it is beyond doubt that the conditions for the use of deadly force were met in this case, at least with respect to the fleeing suspect.
*794The district court went on, however, to discuss whether the officers’ use of deadly force constituted an unreasonable seizure of plaintiff Landol. As noted above, the court felt compelled to deem Fourth Amendment analysis applicable to plaintiffs claim because of our decision in Fernandez v. Leonard, 784 F.2d at 1217, where we had observed that, “All nine Justices [in Garner] agreed that a law enforcement officer ‘seizes’ someone by shooting him.” Fernandez involved a hostage situation in which, according to the plaintiffs’ version of the facts, police officers fired deliberately at an unarmed hostage at least five times, killing him. We denied the defendant’s motion for summary judgment based on qualified immunity, finding that a factual dispute remained concerning whether the seizure-by-shooting had been unreasonable, and thus a violation of the deceased’s Fourth Amendment rights. Id.
The district court in this case followed the Fernandez course. It held that a jury must resolve the factual dispute over whether “the police in this case effected an unreasonable seizure upon plaintiff by shooting him (while attempting to apprehend the suspect), which would amount to a violation of plaintiffs constitutional rights under the Fourth Amendment....” Id. at 8 (emphasis in original). The district court thus concluded that Landol had been “seized” within the meaning of the Fourth Amendment, but it left to the jury the determination whether that seizure was unreasonable.
C.
After the summary judgment decision, but before the trial in this case, the Supreme Court further expounded on the use of excessive force by police officers pursuing a criminal suspect. In Brower v. County of Inyo, 489 U.S. 593, 109 S.Ct. 1378, 103 L.Ed.2d 628 (1989), the fleeing suspect was killed when his car crashed into a police roadblock. His heirs, the plaintiffs, claimed the roadblock had been set up intentionally in such manner as to be likely to kill him. In the course of its decision reversing dismissal of plaintiffs’ complaint, the Court stated that, “[violation of the Fourth Amendment requires an intentional acquisition of physical control.” Id. 109 S.Ct. at 1381 (emphasis added). The Court restated the principle at greater length later in the opinion:
[A] Fourth Amendment seizure does not occur whenever there is a governmentally caused termination of an individual’s freedom of movement ..., nor even whenever there is a governmentally caused and governmentally desired termination of an individual’s freedom of movement ..., but only when there is a governmental termination of freedom of movement through means intentionally applied.
Id. (emphasis in original; other emphasis deleted).
Defendants argue that Brower requires a finding that plaintiff was not seized in this case because he was not the object of the officers’ actions; their intent was to capture the suspect, not to restrain Landol. The plaintiff’s shooting was an unfortunate accident, the officers contend, not a Fourth Amendment violation.
Plaintiff, on the other hand, insists that the district court’s ruling that he was seized by the police bullet that struck him remains valid even after Brower. He emphasizes the statement in Garner that, “[wjhenever an officer restrains the freedom of a person to walk away, he has seized that person,” see 471 U.S. at 7, 105 S.Ct. at 1699. Implicitly at least,6 plaintiff argues that the police actions in this case meet the Brower requirement of intentionality because the officers deliberately fired their weapons at the car containing Landol, with knowledge that he was there.
The explicit language quoted above from Garner, as well as the seizure-by-shooting language from Fernandez, might appear at first glance to support plaintiff’s view that he was “seized” by the police bullet that struck his jaw. Indeed, the Supreme *795Court, just months after Brower, repeated the general proposition that a Fourth Amendment seizure occurs whenever government actors have “in some way restrained the liberty of a citizen,” Graham v. Connor, — U.S. -, 109 S.Ct. 1865, 1871 n. 10, 104 L.Ed.2d 443 (1989).
A closer look at the caselaw, however, persuades us that Landol does not have a Fourth Amendment claim. The Supreme Court in Brower carefully distinguished between police action directed toward producing a particular result — in Fourth Amendment parlance, “an intentional acquisition of physical control” — and police action that simply causes a particular result. Unless the restraint of liberty at issue resulted from an attempt to gain control of the individual, the Court stated, there has been no Fourth Amendment seizure. We think it worth repeating here the Court’s illustration of this distinction:
Thus, if a parked and unoccupied police car slips its brake and pins a passerby against a wall, it is likely that a tort has occurred, but not a violation of the Fourth Amendment. And the situation would not change if the passerby happened, by lucky chance, to be a serial murderer for whom there was an outstanding arrest warrant — even if, at the time he was thus pinned, he was in the process of running away from two pursuing constables. It is clear, in other words, that a Fourth Amendment seizure does not occur whenever there is a gov-ernmentally caused termination of an individual’s freedom of movement (the innocent passerby), nor even whenever there is a governmentally caused and governmentally desired termination of an individual’s freedom of movement (the fleeing felon), but only when there is a governmental termination of freedom of movement through means intentionally applied.
109 S.Ct. at 1381 (emphasis in original).
We reject the notion that the “intention” requirement is met by the deliberateness with which a given action is taken. A police officer’s deliberate decision to shoot at a car containing a robber and a hostage for the purpose of stopping the robber’s flight does not result in the sort of willful detention of the hostage that the Fourth Amendment was designed to govern. The Supreme Court emphasized this point in Brower, noting that “[t]he writs of assistance that were the principal grievance against which the Fourth Amendment was directed ... did not involve unintended consequences of government action,” 109 S.Ct. at 1381 (citations omitted). The Fourth Amendment, the Court concluded, “addresses ‘misuse of power,’ ... not the accidental effects of otherwise lawful government conduct.” Id. (citation omitted).
The language on which plaintiff relies for his broader view of the Fourth Amendment must be read in context. Each of the Supreme Court’s recent cases on the Fourth Amendment, as well as our own Fernandez decision, involved scenarios in which the individual claiming to have been seized had been the direct object of police intervention. In writing the words that plaintiff quotes, the courts unquestionably had in mind that typical frame of reference. The facts of this case are very different, and the discussion in Brower makes it clear that no Fourth Amendment seizure occurred here because Landol was not the object of the police bullet that struck him.7 Indeed, Landol’s presence in the car arguably gave the police officers a more compelling need to stop the suspect than if there had been no hostage; the errant bullet did not in these circumstances transform the police action into a seizure.8 The jury’s verdict therefore may not stand.
*796At this point, we digress a moment to emphasize that our decision does not mean that Fourth Amendment consequences may never result from unintended action. In Brower, the Court referred to a case in which officers mistakenly arrested one man, thinking he was someone else. See Hill v. California, 401 U.S. 797, 802-05, 91 S.Ct. 1106, 1110-11, 28 L.Ed.2d 484 (1971). A seizure occurs in such a case, the Court held, because the detention was intended even though the object of it was not. Similarly, when officers mistakenly shoot an innocent victim thinking that he is the suspect they are pursuing, the seizure was intended even though the target was not. See Grandstaff v. City of Borger, Tex., 767 F.2d 161, 165-68 (5th Cir.1985) (mistaken shooting situation; court analyzes the incident as potential due process violation rather than Fourth Amendment). What is significant about these examples is that the police officers’ actions were directed toward particular individuals; the seizures were mistakes of identity but they were by no means inadvertent “acquisitions of physical control.”9 It is intervention directed at a specific individual that furnishes the basis for a Fourth Amendment claim.
II.
In Graham v. Connor, — U.S. -, 109 S.Ct. 1865, 1871, 104 L.Ed.2d 448 (1989), the Supreme Court held that all claims that law enforcement officials have used excessive force in the course of an arrest or other seizure should be analyzed under the Fourth Amendment and its “reasonableness” standard, rather than under a substantive due process approach. Undoubtedly because of Graham, and the district court’s prior ruling that Landol had been seized, the magistrate who tried this case instructed the jury to determine only whether defendants had committed a Fourth Amendment violation by making an “unreasonable” seizure of Landol.
We assume that claims of excessive force outside the context of a seizure still may be analyzed under substantive due process principles. Accord Pleasant v. Zamieski, 895 F.2d 272, 276 n. 2 (6th Cir.1990). See also Sinaloa Lake Owners Ass ’n v. City of Simi Valley, 882 F.2d 1398, 1408 n. 10 (9th Cir.1989). Thus, while Landol did not have a Fourth Amendment claim, he was entitled to bring a claim under the Fourteenth Amendment alleging a deprivation of “life, liberty, or property” without due process as a result of the police shooting. Landol did not object to the magistrate’s exclusion of a due process claim from this case, but we need not dwell on the issue of waiver because the record establishes as a matter of law that he could not have prevailed with such a claim against appellants.
We have held that government officials may be held liable for a substantive due process violation only if their conduct “reflect[ed] a reckless or callous indifference to an individual’s rights.” Gutierrez-Rodriguez v. Cartagena, 882 F.2d 553, 559 (1st Cir.1989) (quoting Germany v. Vance, 868 F.2d 9, 18 (1st Cir.1989)). Plaintiff has provided no evidence from which a jury could infer such a state of mind on the part *797of either Cruz or Cintron. In this tense, rapidly developing situation, where the fleeing suspect was armed, had threatened to kill his hostage, and had commandeered a car and abducted its driver, the decision to shoot toward the hijacked vehicle, by itself, falls far short of demonstrating reckless or callous indifference toward the hostage’s rights.
To hold that shooting in such circumstances violates the constitutional rights of a hostage whom the officers are trying to free would be to hamstring seriously law enforcement officers in their efforts to resolve explosive situations. It is inevitable that the police response to violent crime will at times create some risk of injury to others, including innocent bystanders. We decline to hold that the mere presence of risk reflects a callous indifference to the constitutional rights of those individuals potentially harmed. Any other conclusion would both chill law enforcement officers in the performance of their duties and encourage hostage-taking and criminal activity in public settings so as to minimize police intervention.
The record reveals no additional facts about this particular shooting that would allow a jury to find a due process violation. The evidence shows that Cruz, who knew there was a hostage, shot only twice at the tires of the car.10 Cintron testified that he fired only once “toward the door of the car” after seeing Cruz shoot, presumably in an exchange of gunfire with the persons in the car, all of whom Cintron believed to be suspects.11
At best, Landol can argue that Cintron acted negligently in firing in a manner that could have caused injury to the occupants of the car without more fully analyzing the circumstances. Negligence, however, is insufficient to establish a due process violation. Daniels v. Williams, 474 U.S. 327, 106 S.Ct. 662, 88 L.Ed.2d 662 (1986); Davidson v. Cannon, 474 U.S. 344, 106 S.Ct. 668, 88 L.Ed.2d 677 (1986).12 Moreover, we question whether Cintron’s actions fall below even a reasonableness standard, being mindful of the Supreme Court’s admonition that “[t]he calculus of reasonableness must embody allowance for the fact that police officers are often forced to make split-second judgments” in trying circumstances, Graham v. Connor, 109 S.Ct. at 1872. See also id. (“The ‘reasonableness’ of a particular use of force must be judged from the perspective of a reasonable officer on the scene, rather than with the 20/20 vision of hindsight.”).13
It is worth considering, for the sake of comparison, the facts of a case in which we upheld a jury’s finding that police officers violated an individual’s due process rights by shooting him. In Gutierrez-Rodriguez, 882 F.2d 553, four plainclothes officers, *798with guns drawn, approached a young couple sitting in their car admiring the view at a secluded spot in a rural, mountainous area. The officers were doing “preventive rounds” in search of drug traffickers. When the young man in the car saw the group of unidentified and armed men approaching, he hastily started his engine and began to drive away. The officers, without warning, began shooting. One bullet struck the young man in the back, damaging his spinal cord and rendering him a paraplegic. The case before us is a far cry from Gutierrez-Rodriguez. See also Fernandez v. Leonard, 784 F.2d at 1211-13 (intentional shooting of unarmed hostage); Grandstaff, 767 F.2d at 165-66 (intentional, though mistaken, shooting of innocent bystander).14
III.
To sum up, we hold that no Fourth Amendment seizure occurred when plaintiff was shot inadvertently during a police pursuit of the robbery suspect who was holding him hostage; the Fourth Amendment is implicated only when the individual alleging harm was the object of the challenged police conduct. Although an individual injured by law enforcement officers outside the context of a seizure may bring a substantive due process cause of action, such a claim fails as a matter of law in the circumstances of this case; plaintiffs evidence is insufficient to establish reckless or callous indifference to his constitutional rights by appellants.
The judgment of the district court therefore is REVERSED and the case is REMANDED to that court for the entry of judgments notwithstanding the verdict for both appellants.