OPINION
{1} This direct appeal addresses the presentment of evidence in the penalty phase of a capital appeal. The Capital Felony Sentencing Act (CFSA), NMSA 1978, §§ 31-20A-1 to -6 (1979, as amended), directs the jury to weigh aggravating and mitigating circumstances to determine the appropriate sentence. The State appeals from the district court’s pretrial ruling that evidence of Defendant’s prior convictions may be admitted during the penalty phase of the trial only if the State first establishes its relevance to the jury’s selection of the sentence. We hold that the district court must facilitate this weighing, on a case-by-case basis, according to the evidentiary rules of relevance and reliability and the CFSA’s statutory directives. Without sufficient information about facts and circumstances that will be at issue during the penalty phase of trial, the district court appropriately reserved ruling on the relevance of the evidence.
I. FACTS
{2} Defendant is charged with one count of first-degree murder, two counts of conspiracy to commit first-degree murder, one count of attempt to commit first-degree murder, two counts of possession of a deadly weapon by a prisoner, one count of tampering with evidence, and one count of unlawful assault on a jail. The State is seeking the death penalty on the following aggravating circumstances:
1. The victim, Ralph Garcia, was a peace officer who was acting in the lawful discharge of an official duty when he was murdered.
2. While incarcerated in a penal institution, the Guadalupe County Correctional Facility, in New Mexico, ... Defendant, with the intent to kill, murdered, Ralph Garcia, who was at the time lawfully on the premises of a penal institution in New Mexico, namely the Guadalupe County Correctional Facility.
See Section 31-20A-5(A), (D).
{3} This appeal concerns Defendant’s motion in limine, in which Defendant sought an order precluding the State from mentioning the name or nature of his prior felony convictions in either the guilt or penalty phase of trial. Defendant argued that his prior convictions are irrelevant to any issue relating to his guilt or potential sentence.
*313{4} The district court held two hearings on Defendant’s motion. At the first hearing, the court stated that the evidence would not be admissible as impeachment evidence during the guilt phase of the trial unless Defendant “opens the door, makes that an issue at trial, or [Defendant takes the stand.”
{5} At the second hearing, the State asked permission to introduce evidence of Defendant’s prior convictions, including the name and nature of the crimes during the penalty phase of the trial in three ways. First, the State sought to introduce evidence of Defendant’s prior convictions “right out of the box,” regardless of Defendant’s presentation of mitigating evidence in the sentencing phase. Second, the State sought permission to cross-examine any of Defendant’s witnesses, “no matter who that witness is,” using Defendant’s prior convictions by asking whether knowledge of the convictions “would ... change [their] opinion of Mr. Sanchez if [they] knew he had a prior conviction for murder.” Third, the State sought permission to ask its own experts on direct examination about Defendant’s prior convictions.
{6} Orally, the district court ruled that the State could not introduce evidence of Defendant’s prior convictions “right out of the box,” and the State cannot bring in the evidence unless the State first establishes its relevance. The court clarified the ruling in its written order:
New Mexico law does not automatically allow introduction of such evidence in the State’s ease[-]in[-]ehief of the “penalty phase,” of Defendant’s trial, unless the State can first establish such evidence is relevant to the sentencing of ... Defendant, once a jury is considering mitigating and aggravating circumstances.
IT IS THEREFORE ORDERED, that the State is prohibited from automatically introducing Defendant’s prior Second[-]Degree Murder conviction, in their case[-]in[-]chief, during the “penalty phase” of Defendant’s trial, unless the State can first establish that such evidence is relevant.
The State appealed the district court’s ruling directly to this Court.
II. JURISDICTION
{7} Defendant argues that this Court does not have jurisdiction over the State’s appeal because the State has no constitutional or statutory right to an appeal from the district court’s order. “Generally, the State cannot appeal proceedings from a judgment in favor of the defendant in a criminal case absent a constitutional provision or statute conferring that right.” State v. Montoya, 2008-NMSC-043, ¶ 10, 144 N.M. 458, 188 P.3d 1209 (internal quotation marks and citations omitted). NMSA 1978, Section 39-3-3(B)(2) (1972) provides the State with a statutory right of appeal from non-final orders, which are generally outside of the State’s constitutional right to appeal. State v. Alvarez, 113 N.M. 82, 85, 823 P.2d 324, 327 (Ct.App.1991).
{8} As it applies to this case, Section 39-3-3(B)(2) has two requirements: (1) the district court order is one “suppressing or excluding evidence or requiring the return of seized property”; and (2) the district attorney certifies “that the evidence is a substantial proof of a fact material in the proceeding.” Defendant argues that the district court order does not meet the first requirement because the order only precludes the State from “automatically” introducing Defendant’s prior conviction. Defendant argues that the order permits the State to introduce evidence upon a showing of relevance and, therefore, is not “suppressing or excluding evidence.”
{9} Defendant further argues that the district court’s order does not meet the second Section 39-3-3(B)(2) requirement because the prior convictions are not “substantial proof of a fact material in the proceeding.” Defendant argues that his prior convictions are neither aggravating nor mitigating circumstances under the CFSA, and that “even if the prior convictions are excluded, the State will still be able to seek the death penalty in this ease.” Therefore, Defendant argues the State does not have a right to an interlocutory appeal from the district court’s order.
{10} In contrast, the State argues that it has both a statutory and a constitutional right to appeal the district court’s order. The State asserts that evidence of Defen*314dant’s prior convictions is material to the issue of sentence selection, and that “[t]he evidence of Defendant’s prior convictions will substantially affect the outcome of the jury’s decision and, therefore, is material to the penalty phase proceeding.” The State argues that by denying its assertion of per se relevance, the district court’s order excluded evidence of Defendant’s prior convictions for purposes of Section 39-3-3(B)(2).
{11} We agree with the State that the district court’s order excluded the per se introduction of Defendant’s prior convictions. Furthermore, the district attorney certified that the evidence is substantial proof of a fact material in the proceeding. Therefore, the State has a statutory right of appeal under Section 39 — 3—3(B)(2). Having determined that the State has a statutory right to an interlocutory appeal, we need not address the State’s argument that it also has a constitutional right to appeal.
III. ADMISSIBILITY OF DEFENDANT’S PRIOR CONVICTIONS
{12} The district court has discretion to determine the admissibility of evidence, and we will not reverse the court’s order absent an abuse of discretion. State v. Hughey, 2007-NMSC-036, ¶ 9, 142 N.M. 83, 163 P.3d 470. This case also involves a threshold determination of the correct evidentiary standard for the penalty phase of a trial under the CFSA. We make that determination de novo. See id.
{13} The State characterizes the primary issue in this ease as “whether a capital defendant’s prior convictions are admissible under the Capital Felony Sentencing Act regardless of the defendant’s mitigation evidence.” The State argues that the CFSA requires the jury to consider facts, other than the aggravating circumstances, in deciding whether to impose the death penalty. Specifically, the State argues that the jury must consider “mitigating circumstances, the relative weight of the mitigating and aggravating circumstances, and the defendant and the circumstances of the crime.” See § 31-20A-2. Therefore, the State argues evidence of Defendant’s prior crimes is relevant to the jury’s selection of the appropriate penalty regardless of Defendant’s presentation of mitigating evidence, and it should be admissible without precondition.
{14} Defendant concedes that, under the CFSA, evidence of his prior convictions may be admissible if Defendant first introduced mitigating evidence to show the lack of a prior criminal record, or to show that he is a peaceful person. However, Defendant argues that the CFSA permits evidence of the enumerated aggravating and mitigating circumstances and of other mitigating circumstances, but it does not instruct the jury to consider non-statutory, aggravating circumstances, or other circumstances in favor of imposing the death penalty. Therefore, Defendant argues that the district court’s order was appropriate.
{15} The penalty phase of trial contains two parts. First, the jury must find one of the enumerated aggravating circumstances, beyond a reasonable doubt, to determine that Defendant is eligible for the death penalty. Jones v. United States, 527 U.S. 373, 381, 119 S.Ct. 2090, 144 L.Ed.2d 370 (1999); see § 31-20A-5. This is known as the “eligibility phase.” Jones, 527 U.S. at 381,119 S.Ct. 2090 (internal quotation marks omitted). Next is the “selection phase,” id. (internal quotation marks omitted), in which Section 31-20A-2(B) provides guidance on how to weigh the evidence permitted under Section 31-20A-KC):
B. After weighing the aggravating circumstances and the mitigating circumstances, weighing them against each other, and considering both the defendant and the crime, the jury or judge shall determine whether the defendant should be sentenced to death or life imprisonment.
Section 31-20A-2(B); see State v. Jacobs, 2000-NMSC-026, ¶ 67, 129 N.M. 448, 10 P.3d 127 (“Section 31-20A-2(B) may not be used to permit the introduction of otherwise inadmissible evidence.”). This section sets out a weighing approach to capital sentencing.
{16} Where the capital sentencing statute directs a weighing of aggravating and mitigating circumstances, the district court must be aware of the possibility that “infection of the process with an invalid aggrava*315ting factor might require invalidation of the death sentence.” Stringer v. Black, 503 U.S. 222, 230, 112 S.Ct. 1130, 117 L.Ed.2d 367 (1992). The Eighth Amendment of the United States Constitution requires that at the heart of the selection phase is “an individualized determination on the basis of the character of the individual and the circumstances of the crime.” Zant v. Stephens, 462 U.S. 862, 878-79, 103 S.Ct. 2733, 77 L.Ed.2d 235 (1983). However, “the Constitution does not require the jury to ignore other possible [non-statutory] aggravating factors in the process of selecting ... those defendants who will actually be sentenced to death.” Id.
{17} Within this context, the rules of relevance, Rules 11-401 and -402 NMRA, the requirement of weighing unfair prejudice against probative value, Rule 11-403 NMRA, and the CFSA, Section 31-20A-1(C), provide the parameters for the evidence that the jury may hear. Section 31-20A-1(C) permits the jury to hear all evidence introduced at trial and any additional evidence as to “the circumstances of the crime and as to any aggravating or mitigating circumstances” enumerated in the CFSA. For example, the State may introduce evidence relevant to the enumerated aggravating factors “right out of the box.” In State v. Martinez, 2006-NMSC-007, 139 N.M. 152, 130 P.3d 731, the aggravating factor at issue was whether the murder was of a “witness to a crime or any person likely to become a witness to a crime, for the purpose of preventing report of the crime or testimony in any criminal proceeding.” See § 31-20A-5(G). The defendant’s motive or reason for killing the victim was key to proving this aggravating factor. Martinez, 2006-NMSC-007, ¶ 12, 139 N.M. 152, 130 P.3d 731. We held that “[a]lthough not as compelling as incriminating statements, a defendant’s prior crimes may be strong circumstantial evidence of a motive to silence.” Id. ¶ 19. Similarly, victim impact evidence is admissible during the penalty phase of trial when it is relevant to the “circumstances of the crime.” State v. Clark, 1999-NMSC-035, ¶ 38, 128 N.M. 119, 990 P.2d 793 (“[V]ictim impact testimony is consistent with the Capital Felony Sentencing Act following Payne because it constitutes additional evidence as to the circumstances of the crime under Section 31-20A-1(C) and [Section 31-20A-2(B)].”); see State v. Allen, 2000-NMSC-002, ¶ 52, 128 N.M. 482, 994 P.2d 728 (“[V]ictim impact evidence, brief and narrowly presented, is admissible during the penalty phase of death penalty cases.” (internal quotation marks and citation omitted)).
{18} Evidence that is irrelevant to aggravating circumstances, mitigating circumstances, or circumstances of the crime is inadmissible unless the defendant first opens the door to that evidence. We recognized this principle in Jacobs when we rejected the State’s argument that certain evidence was probative of Defendant’s lack of remorse. 2000-NMSC-026, ¶ 68,129 N.M. 448,10 P.3d 127. In that case, the Court clarified its holding in Allen, which permitted the State to offer evidence tending to prove that the defendant was unremorseful. In Allen, the Court “construed the argument to have been offered in rebuttal to the defendant’s statement at sentencing in which he had expressed remorse for the killing.” Jacobs, 2000-NMSC-026, ¶ 68,129 N.M. 448,10 P.3d 127. Jacobs held that evidence to show the defendant’s lack of remorse was inadmissible because the defendant had not “opened the door” as he had in Allen. Jacobs, 2000-NMSC-026, ¶ 68, 129 N.M. 448, 10 P.3d 127. Therefore, the issue of remorse was outside the scope of admissible evidence as defined by Section 31-20A-1(C).
{19} The CFSA states that the death penalty shall not be imposed if “the sentence of death was imposed under the influence of passion, prejudice or any other arbitrary factor.” Section 31-20A-4(C)(3). “ ‘It is of vital importance to the defendant and to the community that any decision to impose the death sentence be, and appear to be, based on reason rather than caprice or emotion.’ ” Jacobs, 2000-NMSC-026, ¶ 69, 129 N.M. 448, 10 P.3d 127 (quoting Gardner v. Florida, 430 U.S. 349, 358, 97 S.Ct. 1197, 51 L.Ed.2d 393 (1977)). Thus, the CFSA acknowledges the possibility that the balancing of aggravating and mitigating circumstances may be infected if the sentencing authority considers an invalid aggravating factor. See Stringer, 503 U.S. at 230,112 S.Ct. 1130.
*316{20} On appeal, if the possibility that the jury voted for the death penalty under the influence of an improper circumstance exists, and the Court “cannot say that this evidence did not bear on any juror’s decision to sentence Defendant to death,” we must reverse the sentence and remand for a new sentencing hearing. Jacobs, 2000-NMSC-026, ¶ 69, 129 N.M. 448, 10 P.3d 127; see Clark, 1999-NMSC-035, ¶30, 128 N.M. 119, 990 P.2d 793 (holding that the proportionality determination under Section 31-20A-4 is only performed by the Supreme Court after a sentence of death has been handed down). Keeping this caution in mind, the district court must balance the probative value of relevant evidence against the danger of unfair prejudice. Rule 11-403. Certain evidence may not be admissible, even though it is relevant. Allen, 2000-NMSC-002, ¶ 54, 128 N.M. 482, 994 P.2d 728.
{21} In the present case, the district court did not have enough information to rule on •the admissibility of Defendant’s, prior convictions at sentencing. Whether {and to what extent Defendant’s prior convictions are relevant depends on the facts and circumstances adduced during both the guilt and penalty phases of trial. The court then has to determine whether the evidence’s probative value is substantially outweighed by the danger of undue prejudice. We cannot fault the district court for reserving a ruling on the relevance of these issues without knowing what evidence the State plans to introduce and what facts and circumstances the parties will put at issue in the sentencing phase of the trial. The district court must address the admissibility of the evidence on an individualized, case-by-case basis. We hold that the district court did not abuse its discretion by requiring the State to first establish the relevance of Defendant’s prior crimes before such evidence may be admitted during the sentencing phase of trial.
IV. CONCLUSION
{22} The rules of evidence and the CFSA govern the admissibility of evidence during the penalty phase of capital felony sentencing proceeding. Therefore, the admissibility of evidence is determined by applying these rules within the context of the CFSA. We affirm the district court’s order and remand for further proceedings.
{23} IT IS SO ORDERED.
WE CONCUR: EDWARD L. CHÁVEZ, Chief Justice and PATRICIO M. SERNA, RICHARD C. BOSSON, and CHARLES W. DANIELS, Justices.