*713The petitioner, Vinroy Hines, appeals following the denial of his petition for certification to appeal from the judgment of the habeas court denying his petition for a writ of habeas corpus, in which he challenged his conviction for criminal attempt to commit assault in the first degree in violation of *714General Statutes §§ 53a-49 and 53a-59 (a)(1),1 two counts of assault in the second degree in violation of General Statutes § 53a-60 (a)(2),2 kidnapping in the first degree in violation of General Statutes § 53a-92 (a)(2)(A),3 and criminal violation of a protective order in violation of General Statutes § 53a-223 (a).4 In his petition for a writ of habeas corpus, he claimed that the state had violated his state and federal constitutional rights to due process and a fair trial by failing to disclose favorable evidence to him in violation of Brady v. Maryland, 373 U.S. 83, 87, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), then failing to correct allegedly perjured and misleading testimony relating to that undisclosed evidence in violation of Napue v. Illinois, 360 U.S. 264, 269, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959). In particular, the petitioner asserted that the state failed to disclose an agreement *715between the state and his codefendant, Conray Jones, as to favorable consideration that Jones would receive from the state in exchange for his testimony against the petitioner, then failed to correct Jones' testimony that no such agreement existed. The petitioner *433argued that the agreement not disclosed due to these violations was material to his guilt, and thus that if the jury had been informed of the agreement, it was reasonably probable that it would have reached a different verdict. The habeas court rejected the petitioner's claims by denying his habeas corpus petition, and later denied his petition for certification to appeal. The petitioner appeals from that denial, claiming that the habeas court abused its discretion by so ordering because the issues upon which he challenged his conviction as to which he seeks appellate review are debatable among jurists of reason, the court could have resolved those issues in a different manner than the habeas court, and they raise questions that are adequate to deserve encouragement to proceed further. We disagree with the petitioner, and thus dismiss his appeal.
We set forth the following facts in the petitioner's direct appeal. "The [petitioner] and ... the victim5 were in a romantic relationship and had two children together. The victim and their two children resided in a family shelter in East Hartford, but often stayed with the [petitioner] in his apartment in Bridgeport. On January 1, 2009, the [petitioner] and his cousin, Conray Jones, arrived at the family shelter to take the victim and their children to Bridgeport. On the way to Bridgeport, the group stopped to eat at a restaurant. While sitting next to the victim in the backseat of Jones' car, which was parked outside the restaurant, the [petitioner] began talking to the victim and then suddenly *716struck her on the nose with a beer bottle. Jones then proceeded to drive the group toward Bridgeport. For the first thirty minutes of the drive, the [petitioner] remained in the backseat with the victim and their two children, punching the victim in the head, back and shoulder. Once in the New Haven area, the [petitioner] produced a box cutter and repeatedly stabbed the victim on various parts of her body. He put the box cutter near the victim's face and told her that, when they arrived in Bridgeport, he would 'pop off [her] head and pop off his [own] head.'
"Throughout the ride, the [petitioner] asked Jones to pass him a knife. When Jones told the [petitioner] that he did not have one, the [petitioner] reached into the front of the car and opened the glove compartment in front of the passenger seat. In fear that the [petitioner] was reaching for a knife with which to stab her, the victim slid behind the [petitioner] and jumped out of the car, which was traveling at a speed of sixty-five miles per hour. Jones continued to drive the [petitioner] and the children to Bridgeport. Meanwhile, the victim was rescued from the side of the road by a passing driver who drove the victim to a gas station where she called the police. The victim was taken to the hospital where she was treated for a broken nose and toe, two one-half inch lacerations on her scalp and multiple contusions and abrasions from contact with the road.
"Thereafter, the [petitioner] was arrested and charged by long form information, dated September 15, 2009, with the five aforementioned offenses, and, in addition, two counts of kidnapping in the second degree in violation of General Statutes § 53a-94 (a).... [On September 23, 2009], after the state presented its case-in-chief, the [petitioner] moved for a judgment of acquittal as to all charged crimes. The court granted the motion with respect to the two counts of kidnapping in the second degree, but denied the motion with *434*717respect to the five remaining charges. As a result, the state filed a substitute information, dated September 24, 2009, charging the [petitioner] with the foregoing five counts.
"The [petitioner] then presented his case, which he completed on September 24, 2009.... The case was committed to the jury, which returned a verdict of guilty on all counts contained in the substitute information. The court rendered judgment in accordance with the jury verdict and sentenced the [petitioner] to a total effective sentence of eighteen years in prison and seven years of special parole." (Footnote added.) State v. Hines, 136 Conn.App. 412, 414-17, 44 A.3d 886, cert. denied, 307 Conn. 903, 53 A.3d 219 (2012).
Jones also was arrested for his participation in the events of January 1, 2009. Before he resolved those charges,6 however, he testified against the petitioner and corroborated the victim's version of events. At the time of his testimony, Jones, who was represented by counsel, was incarcerated. The prosecutor, Robin Krawczyk, questioned him about any promises that had been made to him in exchange for his testimony against the petitioner. In response to her questions and to the cross-examination of the petitioner's defense counsel, Jeremy N. Weingast, Jones testified that the state had not made him any promises as to how his case would be handled, but that he hoped and expected that the state would take his cooperation into account at sentencing.7 Following the *435petitioner's trial, on November *71823, 2009, Jones appeared before the trial court for a hearing on a motion to reduce his bond pending the final disposition of the charges against him. Krawczyk told the trial court at that hearing that the state took no position on the proposed bond reduction, explaining her position as follows: "Mr. Jones did testify against *719[the petitioner]. He did testify in the manner in which I expected. He was a key witness. I think it would have been much more difficult for the state to secure a conviction without him." After the court heard this statement, it substantially reduced Jones' bond.
On December 21, 2009, the state assisted Jones a second time by reducing the charges against him from three counts of kidnapping, all felonies, to a single count of providing a false statement in the second degree8 in violation of General Statutes § 53a-157b, a misdemeanor,9 and allowing him to resolve the case against him by pleading guilty to that offense. Two weeks later, on January 4, 2010, when he appeared again for sentencing, Krawczyk informed the court that, although she was not recommending a specific sentence for Jones, she wanted the court to know that he "did testify [at the petitioner's trial] in accordance with what the victim said. And I think he was really important to the state's case because, otherwise, it came down to just her version and his version.... [H]e did corroborate everything including phone calls that were made and [the petitioner's] statements to the people that he was talking to on [the victim's] phone. And all the little details and the little facts that mattered with regards to the charges that the state had to prove were corroborated by Mr. Jones and I think really provided a great deal of help in securing a conviction against [the petitioner]."
*720The court thereafter sentenced Jones to one year of incarceration, execution suspended after five months,10 and an eighteen month conditional discharge.
Following the petitioner's conviction and our affirmance of that conviction on direct appeal, he filed a petition for a writ of habeas corpus. In his amended petition for a writ of habeas corpus, filed on July 18, 2014, he first claimed that his state and federal constitutional rights to due process and a fair trial had been violated by the state's failure to disclose evidence favorable to him. In particular, the petitioner claimed that the state had failed to disclose the consideration that Jones had been *436promised in exchange for his testimony against the petitioner. He claimed that if this evidence had been disclosed by the state and presented to the jury at trial, there was a reasonable probability that he would have been acquitted. His second claim alleged a due process violation on the basis of the state's failure to correct Jones' allegedly false and misleading testimony as to the lack of consideration he had been promised by the state in exchange for his testimony.
The habeas trial was held in Rockville on November 12, 2014. Krawczyk, Weingast, and Jones all testified at trial. Krawczyk described the agreement between the state and Jones as follows: "The agreement always was we would not make any promises to Mr. Jones, but if he testified truthfully, that we would bring his cooperation to the attention of the presiding judge-the presiding pretrial judge-and that that cooperation would be taken into account by that judge with regards to sentencing. And that we would not make a recommendation but only let the judge know ... the relevance of the testimony and the fact that he ... cooperated." Krawczyk said that reducing the charges against Jones *721was not part of their agreement, but that she had decided to reduce the charges against him because of Jones' cooperation and because of her feeling that the petitioner was more culpable than Jones.
Krawczyk testified that she had made a promise to Jones to convey his cooperation against the petitioner to the judge who sentenced him, although the agreement was not set forth in writing before he testified. At first, she recalled relaying this promise to Weingast. When asked for details about that communication, however, she said, "I guess I don't have a particular recollection of relaying it. It's my practice to do that." She admitted, however, that it was possible that she had forgotten to disclose the agreement to Weingast.
When Weingast was questioned about whether he had received notification of an agreement between the state and Jones prior to trial, he testified, "Not that I recall. There may have been a casual ... conversation about it that ... his cooperation would be brought to the sentencing judge's ... attention if and when Mr. Jones was convicted of something." He said that he did not receive any further notification of such an agreement during or after the trial.
Jones also testified at the petitioner's habeas trial. He said that the state never promised to reduce his charges or to inform the judge of his cooperation. Instead, he testified that he hoped that the judge would consider his cooperation.
The habeas court denied the petition for a writ of habeas corpus, concluding that the state had not suppressed evidence of a deal between itself and Jones because "there was no such deal. All the state agreed to do was to remain silent at Mr. Jones' sentencing in regard to a specific sentence and to convey to the sentencing judge the fact that he had cooperated and testified against the petitioner. To the extent that this *722constituted a deal between the state and Mr. Jones11 that deal was communicated to the trial defense counsel and fully explored on the record of the criminal case and laid before the jury that tried the petitioner." (Footnote altered; internal quotation marks omitted.)
In reaching its conclusion, the habeas court made several relevant findings of *437facts, including, inter alia: (1) "On direct examination [at the underlying trial], Krawczyk elicited testimony from Mr. Jones to the effect that there had been no promises of leniency made to him other than the fact that his cooperation and the fact that his testimony against the petitioner would be conveyed to the trial and sentencing judge in his own case as well as the state declining to offer a specific recommendation as to sentencing. Both ... Krawczyk and Mr. Jones reaffirmed that [that] was the extent of the understanding at the habeas trial."; (2) "Krawczyk testified that ... Weingast ... had been informed of this before trial.... Weingast did not recall such advance notice, however."; (3) "Weingast conducted a thorough cross-examination of Mr. Jones and in addition to the comments brought out on direct examination, obtained a concession from Mr. Jones that he 'expected' to receive a favorable consideration for his testimony, not that there was any agreement that he receive consideration."; (4) "This court specifically makes the finding of fact that based upon the totality of the evidence adduced at the habeas trial, there simply is no favorable evidence that was withheld from the defense at the underlying trial. Both sides were diligent and perseverant in ensuring that the entirety of the situation surrounding the testimony of ... Jones was placed in front of the jury trying the petitioner."
The petitioner filed a petition for certification to appeal from the habeas court's denial of his petition *723for a writ of habeas corpus, which the habeas court denied. The petitioner appeals from the denial of his petition for certification to appeal, claiming that the habeas court abused its discretion in denying it. The petitioner argues that there was sufficient evidence to support his constitutional claims that the state had suppressed evidence in violation of Brady, namely, a promise by the state to Jones that it would not oppose his motion to reduce his bond, it would reduce the charges against him, and it would inform the judge of his cooperation, and then failed to correct Jones' allegedly perjured and misleading testimony as to the lack of such an agreement in violation of Napue.
"We begin by setting forth the applicable standard of review and procedural hurdles that the petitioner must surmount to obtain appellate review of the merits of a habeas court's denial of the habeas petition following denial of certification to appeal. In Simms v. Warden, 229 Conn. 178, 187, 640 A.2d 601 (1994), we concluded that ... [General Statutes] § 52-470(b) prevents a reviewing court from hearing the merits of a habeas appeal following the denial of certification to appeal unless the petitioner establishes that the denial of certification constituted an abuse of discretion by the habeas court. In Simms v. Warden, 230 Conn. 608, 615-16, 646 A.2d 126 (1994), we incorporated the factors adopted by the United States Supreme Court in Lozada v. Deeds, 498 U.S. 430, 431-32, 111 S.Ct. 860, 112 L.Ed.2d 956 (1991), as the appropriate standard for determining whether the habeas court abused its discretion in denying certification to appeal. This standard requires the petitioner to demonstrate that the issues are debatable among jurists of reason; that a court could resolve the issues [in a different manner]; or that the questions are adequate to deserve encouragement to proceed further.... A petitioner who establishes an abuse of discretion through one of the factors listed *724above must then demonstrate that the judgment of the habeas court should be reversed on its merits.... In determining whether the habeas court abused its discretion in denying the petitioner's request for certification, we necessarily must consider the merits of the petitioner's underlying *438claims to determine whether the habeas court reasonably determined that the petitioner's appeal was frivolous." (Emphasis in original; internal quotation marks omitted.) Blake v. Commissioner of Correction, 150 Conn.App. 692, 695, 91 A.3d 535, cert. denied, 312 Conn. 923, 94 A.3d 1202 (2014).
"On appellate review, the historical facts found by the habeas court may not be disturbed unless they were clearly erroneous...." (Internal quotation marks omitted.) Rodriguez v. Commissioner of Correction, 131 Conn.App. 336, 343, 27 A.3d 404 (2011), aff'd, 312 Conn. 345, 92 A.3d 944 (2014). "Whether the petitioner's right to due process of law was violated by the nonproduction of possibly exculpatory material, however, is a mixed question of law and fact that warrants plenary review." Milner v. Commissioner of Correction, 63 Conn.App. 726, 736, 779 A.2d 156 (2001).
I
We turn first to the merits of the petitioner's claim that the state suppressed evidence of an agreement between the state and Jones. In support of this claim, the petitioner argues that the evidence was sufficient to show that (1) the state suppressed evidence of an agreement between itself and Jones; (2) the suppressed evidence was favorable to the petitioner; and (3) the suppressed evidence was material to the petitioner's alleged guilt.
"It is well established that suppression by the prosecution of evidence favorable to an accused ... violates due process where the evidence is material either to guilt or to punishment, irrespective of the good faith *725or bad faith of the prosecution. [Brady v. Maryland, supra, 373 U.S. at 87, 83 S.Ct. 1194 ].... To establish a Brady violation the defendant bears the burden of demonstrating: (1) that the prosecution suppressed evidence; (2) that the evidence was favorable to the defense; and (3) that it was material." (Citations omitted; internal quotation marks omitted.) Demers v. State, 209 Conn. 143, 149-50, 547 A.2d 28 (1988).
We first address the habeas court's finding that there was no deal between the state and Jones. We conclude that this finding was clearly erroneous, and is, in fact, belied by the habeas court's finding that "[a]ll the state agreed to do was to remain silent at Mr. Jones' sentencing in regard to a specific sentence and to convey to the sentencing judge the fact that he had cooperated and testified against the petitioner." (Emphasis added.) An agreement by a prosecutor with a cooperating witness to bring the witness' cooperation to the attention of the judge who later sentences the witness on his own pending criminal charges is a deal that must be disclosed to the defendant against whom he testifies, even if the deal does not involve a specific recommendation by the prosecutor for the imposition of a particular sentence. See State v. Ouellette, 295 Conn. 173, 190, 989 A.2d 1048 (2010) ("The importance of candor is particularly acute when a cooperating witness testifies on behalf of the state, which also wields power over that witness' sentencing. As one court has noted, '[i]t is difficult to imagine a greater motivation to lie than the inducement of a reduced sentence....' "); Elsey v. Commissioner of Correction, 126 Conn.App. 144, 152, 10 A.3d 578 ("[a]ny ... understanding or agreement between any state's witness and ... the state's attorney clearly falls within the ambit of Brady principles" [internal quotation marks omitted] ), cert. denied, 300 Conn. 922, 14 A.3d 1007 (2011).
*726We nevertheless conclude that there was sufficient evidence before the *439habeas court to support its conclusion that the state did not suppress evidence favorable to the petitioner in this case. The habeas court reasonably concluded that, to the extent that there was a deal between the state and Jones, the petitioner's counsel was fully informed of it. The record supports this finding through the testimony of Weingast and Krawczyk. Weingast at first said that he did not recall being notified of any agreement between the state and Jones, but then said that there "may have been a casual ... conversation about it that ... his cooperation would be brought to the sentencing judge's ... attention if and when Mr. Jones was convicted of something." The agreement disclosed in that casual conversation was precisely the same agreement that Krawczyk said that she had made with Jones, under which the sentencing judge in Jones' case would be informed of his cooperation in the petitioner's trial. Consistent with Weingast's testimony, Krawczyk testified that it was her usual practice to inform opposing counsel of any such agreement. Moreover, the habeas court was free to credit Krawczyk's testimony that she reduced the charges against Jones of her own volition, and not because it was part of their agreement. On the basis of this testimony, we cannot conclude that the habeas court's finding that defense counsel was informed of any agreement between the state and Jones was clearly erroneous.
"Evidence known to the defendant or his counsel, or that is disclosed, even if during trial, is not considered suppressed as that term is used in Brady. " State v. Dolphin, 195 Conn. 444, 455-56, 488 A.2d 812, cert. denied, 474 U.S. 833, 106 S.Ct. 103, 88 L.Ed.2d 84 (1985). Accordingly, we conclude that the habeas court did not abuse its discretion in denying the petitioner certification to appeal from the dismissal of his claim of a Brady violation. In light of the court's well supported *727factual findings, the issues presented by that claim did not warrant the granting of certification to appeal because they were not "debatable among jurists of reason; [not issues] that a court could resolve [in a different manner]; [and not] questions adequate to deserve encouragement to proceed further." (Emphasis omitted; internal quotation marks omitted.) Blake v. Commissioner of Correction, supra, 150 Conn.App. at 695, 91 A.3d 535.
II
We now turn to the petitioner's claim that the state was required to correct the allegedly perjured testimony of Jones. The habeas court concluded that, to the extent there was a deal between the state and Jones, it was "fully explored on the record of the criminal case and laid before the jury that tried the petitioner."
"It is well established that [i]mpeachment evidence as well as exculpatory evidence falls within Brady 's definition of evidence favorable to an accused.... A plea agreement between the state and a key witness is impeachment evidence falling within the definition of exculpatory evidence contained in Brady ....
"The Supreme Court established a framework for the application of Brady to witness plea agreements in Napue v. Illinois, [supra, 360 U.S. 264, 79 S.Ct. 1173 ], and Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972).... Drawing from these cases, this court has stated: [D]ue process is ... offended if the state, although not soliciting false evidence, allows it to go uncorrected when it appears.... If a government witness falsely denies having struck a bargain with the state, or substantially mischaracterizes the nature of the inducement, the state is *440obliged to correct the misconception.... Regardless of the lack of intent to lie on the part of the witness, Giglio and Napue require that the prosecutor apprise the court when he knows that his witness is giving testimony that is substantially *728misleading.... A new trial is required if the false testimony could ... in any reasonable likelihood have affected the judgment of the jury.'
"The prerequisite of any claim under the Brady, Napue and Giglio line of cases is the existence of an undisclosed agreement or understanding between the cooperating witness and the state.... Normally, this is a fact based claim to be determined by the trial court, subject only to review for clear error." (Citations omitted; emphasis added; internal quotation marks omitted.) State v. Ouellette, supra, 295 Conn. at 185-87, 989 A.2d 1048.
This case does not involve an undisclosed agreement or understanding. See id. Thus, the state was not required under Napue and its progeny to correct Jones' allegedly perjured testimony. As we concluded in part I of this opinion, the record amply supports the finding of the habeas court that the only deal between the state and Jones was fully disclosed to the petitioner's counsel. Accordingly, the petitioner has not met his burden of demonstrating that the issues he sought permission to raise before this court on appeal "are debatable among jurists of reason; that a court could resolve the issues [in a different manner]; or that the questions are adequate to deserve encouragement to proceed further." (Emphasis omitted; internal quotation marks omitted.) Blake v. Commissioner of Correction, supra, 150 Conn.App. at 695, 91 A.3d 535. We therefore conclude that the habeas court did not abuse its discretion in denying the petitioner's petition for certification to appeal on his claim that his due process rights were violated by the prosecution's failure to correct Jones' allegedly perjured testimony.
The appeal is dismissed.
In this opinion the other judges concurred.