delivered the opinion of the court;
The defendant, Alfredo Castro, was charged with possession of more than 30 grams of a substance containing cocaine with intent to deliver and was convicted of that offense in the circuit court of Cook County. The trial court denied defendant’s motion for a new trial and sentenced him to six years in the Illinois Department of Corrections. Defendant now appeals his conviction to this court.
On September 20, 1985, Chicago police officer Frank Garza executed a complaint for a search warrant based on an informant’s tip. Garza requested a search warrant for a male Latin named Alfredo who was approximately 30 years old, 5 feet 3 inches tall, 140 pounds, with brown eyes, a beard and a light complexion. Garza also specified that he wanted to search for cocaine and any controlled substances, as well as any items or documents showing proof of residence. Garza said that *230he had probable cause that the items would be found as stated based on a conversation with a reliable informant. Garza had known the informant for approximately three years and, in the past 18 months, the informant had given Garza information on three separate occasions which had resulted in three separate narcotics raids. Each raid had culminated in arrests and had yielded a substance that tested positively for cocaine.
Relevant to this case, the informant told Garza that he met with Alfredo on September 19, 1985, at Alfredo’s first-floor apartment located at 2915 W. Belden in Chicago, in order to purchase cocaine. Alfredo offered to sell the informant a quarter ounce of cocaine for $425, but the informant asked to sample the cocaine first. The informant told Garza that Alfredo then went to the back of his apartment and returned with a clear plastic bag containing what the informant estimated to be an ounce of cocaine. Next, Alfredo took a small amount of white powder out of the bag and gave it to the informant, who then told Alfredo that he would take it home to try it and, if he was satisfied with its quality, he would return for more. The informant told Garza that he tried the powder and, based on his frequent cocaine use in the past five years, he determined that the substance was cocaine. The informant also told Garza that he believed Alfredo was still in possession of at least one ounce of cocaine.
Based on Garza’s affidavit, the circuit court issued a search warrant for Alfredo and for Alfredo’s first-floor apartment at 2915 W. Belden in Chicago. Four Chicago police officers proceeded to 2915 W. Belden with the warrant. The officers searched the premises and discovered cocaine. When the officers discovered the cocaine, they arrested the defendant, Alfredo Castro.
Before his trial, the defendant filed a motion to suppress the evidence seized pursuant to the search warrant. In his motion, the defendant alleged that: Garza had no reason to believe his informant had ever been inside the defendant’s apartment because Garza made no effort to determine the truth of the informant’s claim; without Garza’s “misleading” affidavit, the search warrant would not have been issued; the warrant failed to state facts sufficient to show probable cause, failed to describe with particularity the person or premises to be searched, and failed to adequately state why a warrant should issue; Garza’s affidavit was based upon uncorroborated hearsay; and Garza’s affidavit contained allegations that were deliberate falsehoods or were made with a reckless disregard for the truth, and those false statements were necessary to a finding of probable cause to search.
Defendant also submitted three affidavits in support of his claim *231that Garza’s affidavit contained falsehoods. Defendant submitted his own affidavit, which stated that he worked from early morning until late afternoon on September 19, 1985, at St. Joseph’s Paper Company, where he had been employed for 13 years. Defendant said that when he returned home on that day, his wife and her family were already home. Defendant claimed that he ate supper, watched television and went to bed. During the time he was home, defendant said, no one came to his home, and, more specifically, no one came to his home to purchase controlled substances.
Carmen Castro, defendant’s wife, also submitted an affidavit in this case. She said that she resided with the defendant at 2915 W. Belden on September 19, 1985. Carmen claimed that she was home throughout the day on September 19 and that the defendant was at work from the early morning until the late afternoon. When the defendant returned home, Carmen said, he ate dinner, watched television and went to bed. Carmen stated that the defendant never left the house once he arrived home from work, and he did not receive any visitors or sell any controlled substances that day.
The third affidavit that defendant submitted was that of his stepson, Luis Munoz. Luis said that he was Carmen’s son and on September 19, 1985, he lived with Carmen and the defendant at 2915 W. Belden. Luis stated that in the late morning or early afternoon of September 19, a man came to the back door of the apartment and asked Luis if he “had anything.” When Luis asked the man what he wanted, the man asked if Alfredo was home. Luis said the man left when Luis told him that Alfredo was not home. Luis stated that he did not give the man anything, nor did anyone in Luis’ presence give the man anything. Finally, Luis said that he was 25 years old, 5 feet 8 inches tall, 170 pounds, with brown eyes and a light complexion. Luis also said that he occasionally wore a beard.
The trial court denied defendant’s motion to suppress and the case proceeded to jury trial. Officers Fernando Correa and Frank Garza both testified for the State. Their testimony was essentially the same and was as follows. Around 4:30 p.m. on September 20, 1985, the officers went to 2915 W. Belden with a search warrant and knocked on the door to the first-floor apartment. A young man answered the door, who the officers later determined was Luis Munoz. When the officers asked if Alfredo was home, Luis said “yes” and walked away. Another man then appeared and said he was Alfredo. The officers showed the defendant their search warrant and entered the apartment. The officers gathered all the occupants of the apartment into the front room and began their search in the front bedroom of the apartment.
*232Upon entering the bedroom, the officers saw an electronic scale, a brown glass jar labeled “Superior Inositol C6 H12 06,” and clear plastic sandwich bags on top of a dresser. Two clear plastic sandwich bags containing white powder were discovered in the top left drawer of that dresser. The officers conducted a field test on the powder which indicated the presence of cocaine. The officers testified that they then placed the defendant under arrest, read him his Miranda rights in English, and asked him to empty his pockets. A small paper packet containing white powder was discovered in the defendant’s wallet.
Following the arrest of the defendant, the officers returned to the front bedroom to continue searching. At this point, the officers said, the defendant told them that he slept in the front bedroom. The second search of the bedroom yielded three more paper packets of white powder, as well as a shoe box containing $5,300 in cash. The officers also found papers with the defendant’s name on them in the bedroom, including a bank statement and a traffic citation. The defendant then asked to speak with the officers and pulled them aside. The defendant told the officers that everything they had found belonged to him. Officer Correa stopped the defendant from speaking and repeated defendant’s Miranda rights in Spanish. The defendant said he understood his rights and again told the officers that the white powder was his and that no one else was involved. Finally, the officers testified that as they were leaving with the defendant, the defendant’s wife said to him, “I told you to stop selling that shit, but you won’t [sic] listen.”
The State also presented the testimony of Gerald Pazin, a forensic chemist for the Chicago police department crime lab. Pazin said that he had examined the evidence in this case and determined that it contained cocaine. Pazin testified that the total weight of the substance containing cocaine was 74.07 grams, or approximately 2lk ounces. Pazin also told the court that the brown glass jar labeled Inositol contained a sugar which, he knew from his experience, was used as a “cutter,” meaning it was used to dilute samples of cocaine or heroin in order to have a larger quantity to sell.
The State rested its case following Pazin’s testimony. Defendant’s first witness was Jeffrey Cole, the assistant controller for the St. Joseph Container Company (which defendant referred to as the St. Joseph Paper Company). Cole testified that the defendant punched out of work at 3 p.m. on September 19, 1985. He punched into work at 6:20 a.m. on September 20, 1985, and punched out again at 3 p.m.
Luis Munoz, defendant’s stepson, also testified on the defendant’s behalf. Luis said that he never heard the defendant ask to speak with the officers, nor did he see the defendant pull the officers aside. In *233addition, Luis told the court that as the officers were leaving with the defendant, his mother said to him (Luis), “I told you about this Luis, to stop, you know messing around with this stuff. Now see what you done [sic] to my husband.” Defendant’s attorney then asked Luis whether, on September 19, 1985, he had been convicted of possession. The State objected, and the trial court sustained the State’s objections. The defendant then made an offer of proof following Luis’ testimony. In the offer of proof, the defendant said that Luis had been convicted on March 27, 1985, of possession of less than 30 grams of cocaine and had been placed on probation for that offense. The defendant conceded, however, that the testimony was not offered to impeach Luis’ testimony, but was offered in an effort to assist the defendant.
The defendant’s wife, Carmen, testified next. She said that she lived with the defendant, Luis, Luis’ fiancee and Ramundo, a cousin, in the apartment at 2915 W. Belden on September 20, 1985. Carmen claimed that she and the defendant shared a bedroom in the back of the apartment, and Luis and his fiancee shared the front bedroom where the cocaine was discovered. Carmen testified that when the officers entered the apartment and gathered the occupants into the front room, they found Luis in the front bedroom. Carmen also denied telling the defendant to “stop selling that shit.” Carmen testified that, as the officers were leaving with the defendant, she told Luis that he had caused her husband this trouble. At this point in Carmen’s testimony, the State objected, and the court sustained the objection. The defendant then made another offer of proof. In this offer of proof, the defendant said that Carmen would testify that her son, Luis, had been placed on probation for possession of less than 30 grams of cocaine nine months before the defendant’s arrest, and as a condition of allowing Luis to live with her, Luis had agreed that he would not have any drugs in the house. Accordingly, Carmen’s statement to Luis when the defendant was arrested indicated that Carmen realized Luis had broken his promise to her.
The defendant also took the stand in his own defense. The defendant said that he was 31 years old in 1985. He testified that he and his wife used the back bedroom of their apartment, and Luis and his fiancee used the front bedroom. The defendant said that he had never used cocaine and denied that he had a packet of cocaine in his wallet when the police arrested him. The defendant also denied telling the police officers that he slept in the front bedroom or that the cocaine belonged to him. The defendant then testified that as the officers were escorting him out, he heard his wife tell Luis, “I told you to stop doing that — you have got [sic] Alfredo into trouble,” but defendant denied that his wife *234said anything to him concerning the cocaine.
Following the defendant’s testimony, the defendant rested his case. Defendant then asked the trial court to instruct the jury on the lesser-included offenses of possession and of possession of less that 30 grams of a substance containing cocaine, in addition to the instruction on possession of more than 30 grams of cocaine with intent to deliver, the crime with which he was charged. The court refused the defendant’s request to instruct the jury on the lesser-included offenses.
The defendant’s case was then submitted to the jury. As the jury was deliberating, it sent the court a note asking whether a person who allows a controlled substance into his house knowingly has constructive possession of that substance. The judge told the jury that he would not answer that question because he would be deciding the case for them if he did so. The jury found the defendant guilty of possession of more than 30 grams of a controlled substance containing cocaine, with intent to deliver. The trial court entered judgment on the verdict and sentenced the defendant to six years’ imprisonment. The trial court denied defendant's motion for a new trial and this appeal followed.
The defendant raises four issues on appeal. The defendant claims that the trial court committed reversible error in refusing to instruct the jury on the lesser-included offenses of possession and possession of less than 30 grams of a substance containing cocaine, the trial court committed reversible error when it denied him an evidentiary hearing on his motion to suppress, the trial court committed reversible error when it refused to allow him to introduce testimony of his stepson’s prior conviction for possession of cocaine, and the State failed to prove him guilty beyond a reasonable doubt.
We first address the defendant’s claim that the trial court committed reversible error in refusing to instruct the jury on the lesser-included offenses of possession of cocaine or possession of less than 30 grams of cocaine. The defendant claims that there was sufficient evidence for the jury to conclude that the defendant possessed the cocaine but did not have the requisite intent to distribute, or that he possessed only the cocaine found in his wallet, which was only .10 grams. The State, however, denies that the defendant was entitled to an instruction on the lesser-included offenses.
In certain cases, a defendant may be entitled to have the jury instructed on a less serious offense that is included within the offense with which he is charged. (People v. Bryant (1986), 113 Ill. 2d 497, 502, 499 N.E.2d 413, 415.) The reason for allowing an instruction on a lesser-included offense is to provide “an important third option to a jury which, believing that the defendant is guilty of something but *235uncertain whether the charged offense has been proved, might otherwise convict rather than acquit the defendant of the greater offense.” (Bryant, 113 Ill. 2d at 502, 499 N.E.2d at 415.) Instructions on lesser-included offenses are not required in every case, however, because the evidence presented in a particular case might rationally preclude instruction on a lesser-included offense. (Bryant, 113 Ill. 2d at 507, 499 N.E.2d at 417.) A lesser-included offense instruction is proper when the evidence would permit a jury rationally to find a defendant guilty of the lesser-included offense and acquit him of the greater offense, and when the greater offense charged would require the jury to find a disputed factual element which is not required for conviction on the lesser-included offense. Bryant, 113 Ill. 2d at 507, 499 N.E.2d at 417-18.
Based on the facts of this case, we conclude that the defendant was entitled to instructions on the lesser offense of possession of less than 30 grams of cocaine. We believe the jury’s note to the trial judge concerning constructive possession shows that the jury believed the defendant was guilty of something but was uncertain whether the offense charged had been proved. Further, the evidence here was sufficient to permit the jury to find the defendant guilty of either of the lesser offenses and to acquit him of the greater offense. Here, conviction of the greater offense, possession of more than 30 grams of cocaine with intent to deliver, would require the jury to decide a disputed fact, viz., whether the defendant or Luis used the front bedroom, a fact that was not required for a conviction of possession of less than 30 grams of cocaine. This was also not a case where an instruction on the lesser offense would have allowed the jury to reach a compromise verdict. (Cf. People v. Zipprich (1986), 141 Ill. App. 3d 123, 127-28, 490 N.E.2d 8, 12.) Accordingly, we find that the trial court committed reversible error in refusing to give this lesser tendered instruction and, therefore, we remand the case for a new trial.
Inasmuch as the defendant must be tried again, we deem it appropriate to consider here those questions raised by the defendant that are likely to recur on retrial. Defendant also contended in this appeal that he was entitled to an evidentiary hearing under Franks v. Delaware (1978), 438 U.S. 154, 57 L. Ed. 2d 667, 98 S. Ct. 2674, on his claim that Officer Garza’s affidavit, upon which the search warrant was issued, contained false statements. Defendant claims that he made a substantial preliminary showing that the warrant affidavit in this case contained false statements because he submitted three affidavits directly contradicting the information contained in Officer Garza’s affidavit. Defendant thus concludes that since he made such a preliminary *236showing, the trial court had no choice under Franks except to hold an evidentiary hearing. Accordingly, defendant asserts that the trial court committed reversible error when it refused his request for an evidentiary hearing.
In response, the State argues that the trial court properly denied defendant’s request for an evidentiary hearing. The State alleges that the defendant failed to make a substantial preliminary showing that the warrant affidavit was false since the defendant did not deny each and every factual allegation in Garza’s affidavit, did not challenge the integrity of Garza’s oath as a whole, and did not challenge any specific allegations in Garza’s affidavit. The State further argues that even if the defendant made a substantial preliminary showing of falsehood, the defendant was not entitled to an evidentiary hearing because the remainder of Garza’s affidavit was sufficient to establish probable cause.
In Franks, the United States Supreme Court held that, under certain circumstances, a defendant may be entitled to an evidentiary hearing to challenge the veracity of statements in a warrant affidavit. (Franks, 438 U.S. 154, 57 L. Ed. 2d 667, 98 S. Ct. 2674.) The Franks Court held that a defendant would be entitled to an evidentiary hearing if he “makes a substantial preliminary showing that a false statement knowingly and intentionally, or with reckless disregard for the truth, was included by the affiant in the warrant affidavit, and if the allegedly false statement is necessary to the finding of probable cause.” (Franks, 438 U.S. at 155-56, 57 L. Ed. 2d at 672, 98 S. Ct. at 2676.) The Court also held that the challenge to the warrant affidavit must be more than conclusory, because a warrant affidavit is presumptively valid and, therefore, a defendant must specifically point out those portions of the affidavit alleged to be false, in an offer of proof, accompanied by a statement of supporting reasons. Franks, 438 U.S. at 171, 57 L. Ed. 2d at 682, 98 S. Ct. at 2684.
The Illinois Supreme Court has accepted these principles as set forth in the Franks decision, but has refused to extend Illinois law beyond Franks, and in fact specifically overruled an Illinois Appellate Court decision which ruled that a warrant executed pursuant to an affidavit containing any false statement must be quashed. (See People v. Lucente (1987), 116 Ill. 2d 133, 145, 506 N.E.2d 1269, 1274, overruling People v. Garcia (1982), 109 Ill. App. 3d 142, 440 N.E.2d 269.) In Lucente, the supreme court held that a defendant’s challenge to a warrant affidavit based on an alibi-type preliminary showing could, in some cases, be sufficient to entitle a defendant to an evidentiary hearing. (Lucente, 116 Ill. 2d 133, 506 N.E.2d 1269.) However, the determi*237nation of whether a defendant has made a substantial showing sufficient to trigger an evidentiary hearing is within the trial court’s discretion and will not be disturbed on review absent an abuse of discretion. (Lucente, 116 Ill. 2d at 152-53, 506 N.E.2d at 1277.) The Lucente court held in that case that the defendant’s preliminary showing there was sufficient to entitle the defendant to an evidentiary hearing, even though it was an alibi-type showing, because the defendant had presented the court with his own affidavit, along with the affidavits of his wife and his sister, and those affidavits were sufficiently detailed so as to subject the affiants to penalties for perjury if their statements were untrue. Lucente, 116 Ill. 2d 133, 506 N.E.2d 1269.
In a recent decision, this court clarified that the Lucente decision did not mandate a Franks hearing in every factually similar case. (People v. Tovar (1988), 169 Ill. App. 3d 986, 523 N.E.2d 1178.) In fact, the supreme court had recognized in Lucente that because the determination of whether to grant a hearing is unavoidably subjective, there may be some cases where a trial court denies a hearing when in fact a warrant was issued on the basis of false statements, and other cases where a hearing is granted and was not warranted. (Lucente, 116 Ill. 2d at 153, 506 N.E.2d at 1277.) However, so long as the trial court exercised its discretion within permissible limits, its judgment should not be disturbed on appeal. (Lucente, 116 Ill. 2d at 153, 506 N.E.2d at 1277.) In Tovar, the court noted that both Lucente and the case before it “involved a complaint for a search warrant based on a confidential informant’s claim that a drug sale had taken place at the defendant’s residence, and both defendants sought a Franks hearing by setting up an alibi, corroborated in this [the Tovar] case by defendant’s wife, and in Lucente by defendant’s wife and sister.” (Tovar, 169 Ill. App. 3d at 992, 523 N.E.2d at 1182.) Despite the similarities to Lucente, however, the Tovar court held that the defendant was not entitled to an evidentiary hearing. The court concluded that the defendant was not entitled to an evidentiary hearing because the affidavits the defendant had submitted were from interested parties, a factor which the Lucente court held weakened the affidavits; the affidavits did not establish that it was impossible for the informant to have had access to the defendant’s apartment, but instead were “I didn’t do it” type affidavits, which the Lucente court found insufficient; and there was no evidence that the State had been uncooperative or evasive as the State had been in Lucente, a factor that the Lucente court found important in granting a hearing. Tovar, 169 Ill. App. 3d at 992, 523 N.E.2d at 1182.
We find this case to be factually similar to Lucente and Tovar. This case involved a complaint for a search warrant based on an in*238formant’s claim that a drug deal had taken place at the defendant’s apartment. The defendant here also sought a Franks hearing based on an alibi defense. Similarly the affiants here, defendant, his wife and his stepson, were interested parties. Moreover, in Tovar, the affidavits submitted by defendant did not establish that it was impossible for Garza’s informant to have had access to the defendant’s apartment, but were “I didn’t do it” type affidavits. There is also no evidence here that the State was uncooperative or evasive, in contrast to Lucente, where the State repeatedly failed to produce documents requested by the defendant which would have supported the officer’s affidavit.
Based on the foregoing, we conclude that the trial court properly denied defendant’s request for an evidentiary hearing. The facts presented here are more analogous to those in Tovar, where we upheld the trial court’s exercise of discretion in denying the defendant’s request for an evidentiary hearing. We also find that the trial court did not abuse its discretion here in denying defendant’s request for a Franks hearing.
The defendant further claimed in this appeal that the trial court committed reversible error when it refused to allow the defendant to introduce evidence that his stepson, Luis, was on probation for possession of cocaine at the time of the defendant’s arrest, and when it refused to allow Carmen Castro to testify concerning what she said to Luis when the defendant was arrested. Defendant claims that this information was relevant because it would have shown that Luis, and not the defendant, was the party in possession of the cocaine found in the defendant’s apartment. The defendant contends he was prejudiced by the trial court’s ruling, and that this prejudice was evident because the jury asked the court, as it was deliberating, whether a person who knowingly allows a controlled substance in his house thereby has constructive possession of that substance.
The State contends that the trial court’s rulings concerning Luis’ prior conviction and Carmen’s statements to Luis were properly excluded. The State argues that the evidence was properly excluded because it was not offered to impeach Luis’ credibility, which the State concedes would have been a proper purpose, but was offered to show that it was likely that Luis, rather than the defendant, was the guilty party because of his prior conviction, which was not a proper purpose.
A defendant may try to prove that someone else committed the crime for which he is charged, within limitations. (People v. Ward (1984), 101 Ill. 2d 443, 455, 463 N.E.2d 696, 701-02.) The test of whether evidence is admissible is whether the evidence tends to prove the offense charged and whether it is relevant, i.e., whether it tends to *239make the question of guilt more or less probable. (Ward, 101 Ill. 2d at 455, 463 N.E.2d at 702.) Evidence may be rejected as irrelevant and of little probative value if it is remote, uncertain or would possibly cause unfair prejudice. (Ward, 101 Ill. 2d at 455, 463 N.E.2d at 702; People v. Columbo (1983), 118 Ill. App. 3d 882, 971, 455 N.E.2d 733, 797.) Furthermore, the trial court has broad discretion in ruling on materiality and relevancy issues, and its ruling should be reversed only upon a showing that the trial court abused its discretion. Ward, 101 Ill. 2d at 455-56, 463 N.E.2d at 702; Columbo, 118 Ill. App. 3d at 971, 455 N.E.2d at 797.
In this case, the trial court, by denying the defendant’s offer of proof, apparently held that the defendant’s claim that the cocaine belonged to Luis Munoz was too speculative and was irrelevant to the present case. We agree. As the trial court noted, although the defendant contended that the cocaine here belonged to Luis because Luis used the front bedroom where the cocaine was discovered, Luis himself never admitted, in his affidavit or in his testimony, that he used the front bedroom. In fact, according to the police officers, the defendant admitted to them that he used the front bedroom and that the cocaine was his. Further, any prejudicial effect in limiting the evidence of Luis’ prior conviction was likely minimal, since the jury heard Carmen, Luis and the defendant each testify that Carmen allegedly accused Luis of keeping the cocaine in the apartment. Accordingly, the evidence of Luis’ prior conviction for possession of cocaine was of little probative value and, therefore, the trial court did not abuse its discretion in excluding the evidence.
Finally, the defendant contends that the State failed to prove him guilty beyond a reasonable doubt. We disagree and conclude that there was sufficient evidence to support the jury’s verdict. Our determination, however, concerning the sufficiency of the evidence here is not binding on retrial and is meant only to avoid subjecting the defendant to double jeopardy. See People v. Taylor (1979), 76 Ill. 2d 289, 309-10, 391 N.E.2d 366, 375; People v. Taylor (1987), 163 Ill. App. 3d 346, 362, 516 N.E.2d 649, 659.
Accordingly, for all of the above reasons, the judgment of the circuit court of Cook County is reversed and the cause is remanded for further proceedings consistent with this opinion.
Reversed and remanded.
EGAN, P.J., and McNAMARA, J., concur.