
987 S.W.2d 680 (1999)
337 Ark. 105
Rafael CAMARGO, Appellant,
v.
STATE of Arkansas, Appellee.
No. CR 98-772.
Supreme Court of Arkansas.
March 25, 1999.
*682 Robert C. Marquette, Van Buren, for Appellant.
Mark Pryor, Attorney General, Kelly K. Hill, Deputy Attorney General, David R. Raupp, Senior Assistant Attorney General, Little Rock, for Appellee.
DONALD L. CORBIN, Justice.
Appellant Rafael Camargo appeals the judgment of the Crawford County Circuit Court sentencing him to death for the murders of Deanna Petree and her fifteen-month-old son, Jonathan Macias. This is the second appeal of this matter; hence, our jurisdiction is pursuant to Ark. Sup.Ct. R. 1-2(a)(7). See Camargo v. State, 327 Ark. 631, 940 S.W.2d 464 (1997) (Camargo I). In the first appeal, this court affirmed Appellant's capital-murder convictions, but reversed his death sentence and remanded the case for resentencing. On remand, Appellant was again sentenced to death. Appellant raises two points for reversal of the sentence. We find no error and affirm the judgment.
The pertinent facts were set out in Camargo I:
Appellant Rafael Camargo was convicted of two counts of capital murder and sentenced to death. On October 31, 1994, he killed his former girlfriend, Deanna Petree, and her fifteen-month-old son, Jonathan. The crimes took place in the home Deanna and Jonathan shared with her mother and three brothers. Her mother and two of the brothers testified that they saw appellant shoot Deanna. Robert, the oldest brother, testified that appellant also pointed the shotgun at him and pulled the trigger; but the gun failed to fire. All the survivors took refuge outside the house and heard additional shots being fired. They saw appellant flee from the house before the police arrived. When the police arrived, they found Deanna and Jonathan shot to death in the house.
327 Ark. at 634-35, 940 S.W.2d at 466. This court reversed Appellant's death sentence due to the jury's failure to unanimously return written findings that: (1) one or more aggravating circumstances existed beyond a reasonable doubt; (2) the aggravating circumstances outweighed beyond a reasonable doubt all mitigating circumstances found to exist; and (3) the aggravating circumstances justified a sentence of death beyond a reasonable doubt. See Ark.Code Ann. § 5-4-603(a) (Repl.1997).
During the resentencing trial, the State presented evidence and exhibits that were nearly identical to those presented in the first trial. The jury unanimously found that two aggravating circumstances existed beyond a reasonable doubt: (1) Appellant previously committed another felony, an element of which was the use or threat of violence to another person or creating a substantial risk of death or serious physical injury to another person, and (2) in the commission of capital murder, Appellant knowingly created a great risk of death to a person other than the victims. The jury also unanimously found the mitigating circumstance that Appellant adjusts well to confinement; no other mitigating circumstances were found by any of the jurors. For reversal of the current death sentence, Appellant raises issues concerning the constitutionality of section 5-4-603(a) and the trial court's refusal to specifically instruct the jury on the mitigating factor of Appellant's mental retardation.
I. Constitutionality of Section 5-4-603(a)
For his first point for reversal, Appellant argues that section 5-4-603(a) is unconstitutional because it mandates the imposition of the death penalty and does not allow the jury to show mercy for the defendant. This court has addressed this same argument on numerous occasions, and we have repeatedly upheld the constitutionality of section 5-4-603(a), which provides:
(a) The jury shall impose a sentence of death if it unanimously returns written findings that:
(1) Aggravating circumstances exist beyond a reasonable doubt; and

*683 (2) Aggravating circumstances outweigh beyond a reasonable doubt all mitigating circumstances found to exist; and
(3) Aggravating circumstances justify a sentence of death beyond a reasonable doubt. [Emphasis added.]
Appellant's argument focuses on the word "shall" in support of his argument that if the jury makes those three findings, it has no choice but to impose the death penalty. We disagree.
Section 5-4-603(a) does provide that the jury "shall" impose the death penalty, but only if the jury makes the foregoing three written findings. Greene v. State, 335 Ark. 1, 977 S.W.2d 192 (1998). The jury may show mercy to the defendant "simply by finding that the aggravating circumstances, even though they exist and `outweigh' the mitigating circumstances, do not `justify' imposition of the death sentence." Id. at 33, 977 S.W.2d at 207-08. See also Echols v. State, 326 Ark. 917, 936 S.W.2d 509, cert. denied, 520 U.S. 1244, 117 S.Ct. 1853, 137 L.Ed.2d 1055 (1997) (holding that section 5-4-603(a) merely provides specified criteria that must be fully satisfied before the death penalty can be imposed; it does not contain a binding instruction nor require a mandatory death sentence); Nooner v. State, 322 Ark. 87, 107, 907 S.W.2d 677, 687 (1995), cert. denied, 517 U.S. 1143, 116 S.Ct. 1436, 134 L.Ed.2d 558 (1996) (holding that "[w]e have underscored that our statute provides that a jury is free to sentence to life without parole if it finds the aggravating circumstances do not `justify' death.") Appellant has given us no reason for retreating from our previous holdings, and we decline to do so.
Additionally, the State contends that we could summarily affirm this issue by employing the law-of-the-case doctrine. Particularly, the State contends that because this argument was raised by Appellant during the first trial, the decision in Camargo I is dispositive of the issue, as this court reviewed all alleged errors that may have been prejudicial to Appellant pursuant to Ark. Sup.Ct. R. 4-3(h) and found no such error. Thus, the State argues that the 4-3(h) review is now the law of the case on this issue.
The law-of-the-case doctrine ordinarily arises in the case of a second appeal and requires that matters decided in the first appeal be considered concluded. Davis v. State, 325 Ark. 96, 925 S.W.2d 768 (1996) (citing Fairchild v. Norris, 317 Ark. 166, 876 S.W.2d 588, cert. denied, 513 U.S. 974, 115 S.Ct. 448, 130 L.Ed.2d 357 (1994)). The doctrine is not inflexible and does not absolutely preclude correction of error, but it prevents an issue raised in a prior appeal from being raised in a subsequent appeal "unless the evidence materially varies between the two appeals." Kemp v. State, 335 Ark. 139, 142, 983 S.W.2d 383, 385 (1998) (quoting Fairchild, 317 Ark. at 170, 876 S.W.2d at 590). The doctrine precludes the trial court on remand from considering and deciding questions that were explicitly or implicitly determined on appeal. Foreman v. State, 328 Ark. 583, 945 S.W.2d 926 (1997). Questions that have not been decided do not become law of the case merely because they could have been decided; at the same time, however, law-of-the-case principles are applied when a court concludes that an issue was resolved implicitly despite the lack of any explicit statement. Id. Significantly, the doctrine extends to issues of constitutional law. Kemp, 335 Ark. 139, 983 S.W.2d 383.
It is the State's contention that when this court conducted its review of the record pursuant to Rule 4-3(h), it implicitly decided the constitutional issue now raised by Appellant. We agree that our 4-3(h) review of the record in Camargo I would serve as an additional ground for affirming this issue.
Pursuant to Rule 4-3(h), in all criminal appeals where the appellant has been sentenced to death or life imprisonment, this court must review the record for any adverse rulings objected to by the appellant, but not argued on appeal. This court conducted such a review in Camargo I and found no reversible errors. The record demonstrates that Appellant raised the issue of the constitutionality of section 5-4-603(a) during the first trial. The record also demonstrates that the evidence presented in the second trial did not materially vary with that presented in the first trial. Thus, this court's *684 Rule 4-3(h) review in the first appeal is now the law of the case on this issue.

II. Instruction on Mitigating Factor
For his second point for reversal, Appellant argues that the trial court erred in refusing to instruct the jury on each of the mitigating factors claimed by him. Although he admits that he was allowed to present evidence from a psychiatrist indicating that he functions in a borderline to mild retardation range, Appellant nonetheless argues that it was error for the trial court to refuse to specifically instruct the jury to consider mental retardation as a mitigating circumstance. We disagree.
The record reflects that the trial court instructed the jurors regarding the finding of mitigating circumstances as follows:
If you do unanimously find one or more aggravating circumstances, you should then complete Form 2, which deals with mitigating circumstances. Form 2 lists some factors that you may consider as mitigating circumstances. However, you are not limited to this list. You may, in your discretion, find, other mitigating circumstances.

Unlike an aggravating circumstance, you are not required to be convinced of the existence of a mitigating circumstance beyond a reasonable doubt. A mitigating circumstance is shown if you believe from the evidence that it probably existed. [Emphasis added.]
The trial court then submitted the following mitigating factors to the jurors from Form 2:
The capital murder was committed while [Appellant] was under extreme mental or emotional disturbance.
The capital murder was committed while [Appellant] was acting under unusual pressures or influences or under the domination of another person.
The capital murder was committed while the capacity of [Appellant] to appreciate the wrongfulness of his conduct or to conform his conduct to the requirements of law was impaired as a result of mental disease or defect, intoxication, or drug abuse.
The youth of [Appellant] at the time of the commission of the capital murder.
The capital murder was committed by another person and [Appellant] was an accomplice and his participation relatively minor.
[Appellant] had no significant history of prior criminal activity at the time of the murder.
Other: Specify in writing:
Appellant's proffered instruction contained the first four mitigating factors given by the trial court and the following additional factors:
[Appellant] is remorseful for the commission of this offense.
[Appellant] has demonstrated his ability to adjust to confinement.
[Appellant] functions in the Borderline to Mild Mental Retardation range of intellectual functioning.
Other (specify in writing): [Appellant] cooperated with police by making a statement and assisting in the recovery of evidence or property.
[Appellant], although legally responsible, suffers from an intellectual deficit to some degree.
[Appellant] has a good work history.
The jury found only one mitigating circumstance, that Appellant adjusts well to confinement. Significantly, that mitigating factor was not specifically listed on Form 2, but rather, was written in by the jury foreperson under the category of "Other." Thus, the jury obviously considered the mitigating evidence, given that they found one mitigating circumstance, and obviously considered more factors than just those listed on Form 2. Despite this, Appellant contends that it was error for the trial court to refuse to instruct the jury on the specific mitigating factors submitted on his proffered jury form. The State again asserts that this argument was previously rejected in Camargo I and is now the law of the case.
In Camargo I, this court elected to address Appellant's remaining arguments regarding sentencing to provide guidance for the trial court on remand. One of the issues *685 addressed was Appellant's argument that the trial court erred in refusing to submit a modified instruction form of mitigating circumstances that included Appellant's mental retardation as a mitigating factor. This court rejected Appellant's argument, holding:
Appellant relies upon a line of United States Supreme Court cases that hold that any death sentence resulting from a deliberate exclusion of any mitigating circumstance is presumptively invalid. Penry v. [Lynaugh], 492 U.S. 302, 109 S.Ct. 2934, 106 L.Ed.2d 256 (1989); Hitchcock v. Dugger, 481 U.S. 393, 107 S.Ct. 1821, 95 L.Ed.2d 347 (1987); California v. Brown, 479 U.S. 538, 107 S.Ct. 837, 93 L.Ed.2d 934 (1987); Eddings v. Oklahoma, 455 U.S. 104, 102 S.Ct. 869, 71 L.Ed.2d 1 (1982); Roberts v. Louisiana, 431 U.S. 633, 97 S.Ct. 1993, 52 L.Ed.2d 637 (1977); Gregg v. Georgia, 428 U.S. 153, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976). We find no such deliberate exclusion, because appellant was permitted to make his argument to the jury. We rejected an identical argument in Sheridan v. State, 313 Ark. 23, 852 S.W.2d 772 (1993), in which we held that when the defendant is allowed to present the possible mitigators and the jury is told it is not limited to the mitigators listed on the form, it is not error to submit the standard form to the jury in lieu of a form proposed by the defendant. Id. at 38, 852 S.W.2d at 779.
327 Ark. at 645-46, 940 S.W.2d at 471-72 (emphasis added).
In Sheridan, 313 Ark. 23, 852 S.W.2d 772, relied upon in Camargo I, this court examined the constitutional ramifications of failing to allow the defendant to introduce any relevant mitigating evidence:
In Penry [v. Lynaugh, 492 U.S. 302, 109 S.Ct. 2934, 106 L.Ed.2d 256 (1989)], the United States Supreme Court found that a criminal defendant's Eighth Amendment prohibition upon the infliction of cruel and unusual punishment is violated where he is sentenced to death and no instructions were given informing the jury that it could consider and give effect to mitigating evidence of the defendant's mental retardation and former abuse received. The United States Supreme Court has held that it is a mandatory safeguard of the Eighth Amendment for the sentencing body to be allowed to consider any mitigating factor that is relevant to the particular offender's case. The defense must be allowed during the sentencing phase to introduce any relevant mitigating evidence the defense proffers concerning the character or history of the offender or the circumstances of the offense. Not only must relevant mitigating evidence be admitted, it must be actually considered, which in appropriate cases means specifically instructing the jury to do so. In other words, any death sentence that results from a deliberate exclusion of any relevant mitigating evidence is presumptively invalid.
Applying these U.S. Supreme Court rules to the instant case, it is clear to us that the jury was not limited to the mitigating factors listed on Form 2 but was invited by the judge to consider any others they saw fit and to write them in the blank spaces provided in each category. Therefore, the submission of Form 2 to the jury instead of the form proffered by Sheridan did not act as an impermissible exclusion of relevant mitigating factors. The court specifically told the jurors that the mitigating factors listed were not the sole ones to be considered and that they could consider other factors.
Id. at 37-38, 852 S.W.2d at 779-80 (citations omitted). Accordingly, because we considered and decided in Camargo I the same constitutional argument raised in the instant appeal, our prior decision with regard to that matter is binding in this subsequent appeal from Appellant's resentencing trial.
Appellant also raises two additional points regarding the instructions on mitigating circumstances, neither of which has any merit. First, Appellant argues that the jury, "being extremely cautious to avoid the fate of the last jury which failed to properly execute the verdict forms," failed to consider any mitigating circumstances not enumerated on the instruction forms. This argument is without merit, as noted above, as the one mitigating circumstance unanimously found by the jury, that Appellant adjusts well to *686 confinement, was not enumerated on the instruction forms.
Second, Appellant argues that the fact that the jury executed AMCI 2d 1009, stating that it did not unanimously find by a preponderance of the evidence that Appellant was mentally retarded at the time he committed the murders, indicates that the jury perceived that its findings on that form precluded it from considering the evidence of his mental retardation or intellectual deficit as mitigating factors. We find no merit to this argument, as the trial court specifically instructed the jury on AMCI 2d 1009EXP, which provides in pertinent part:
If you unanimously find that [Appellant] was mentally retarded when the offense was committed, you will sentence him to life imprisonment without parole.
You should consider any evidence with respect to mental retardation first. Then, if you do not unanimously find that [Appellant] has proved mental retardation by a preponderance of the evidence, you should consider the evidence presented on the issue of mental retardation in your deliberations on aggravating and mitigating circumstances. [Emphasis added.]
Clearly, the jury was instructed that it could consider the evidence of Appellant's mental retardation as a mitigating circumstance even if it concluded that Appellant had not proven mental retardation by a preponderance.

III. Rule i-3(h)
In accordance with Rule 4-3(h), the record has been reviewed for adverse rulings objected to by Appellant but not argued on appeal, and no such reversible errors were found. For the aforementioned reasons, the judgment is affirmed.
