This is an appeal from the denial of a writ of habeas corpus. The question presented is whether the district court committed reversible error when, in 2002, it dismissed a group of eight ineffective assistance claims on the ground that the claims had been procedurally defaulted.

Under our 2003 decision in Adams v. Holland, 330 F.3d 398 (6th Cir. 2003), cert. denied, — U.S. —, 124 S.Ct. 1654, 158 L.Ed.2d 392 (2004), the failure of the petitioner herein to raise his ineffective assistance claims before the state supreme court did not result in a procedural default. Only some of the claims had been raised before the state appellate court, however, while others had not. The claims not raised before the intermediate court were clearly defaulted. We shall therefore affirm the challenged judgment in part, reverse it in part, and remand the case for consideration of the non-defaulted claims on their merits.

I

The petitioner, Raymond Covington, was convicted in a Tennessee court in 1991 on charges of armed robbery and murder. The convictions were affirmed on direct appeal.

Mr. Covington then petitioned the state trial court for post-conviction relief. The trial court denied the petition, the Tennessee Court of Criminal Appeals affirmed, and the Tennessee Supreme Court denied an application for discretionary review.

In due course Mr. Covington filed a habeas petition in federal district court. The petition was dismissed without prejudice, but a panel of this court vacated the dismissal and remanded the case for consideration of Covington’s claims. See Covington v. Mills, No. 98-5879, 1999 WL 96646 (6th Cir. Feb. 4,1999).

On remand, the district court concluded that the majority of the claims, including eight of nine subclaims of ineffective assistance of trial counsel, were procedurally defaulted when Covington failed to raise them in his discretionary review application to the Tennessee Supreme Court. The district court rejected the non-defaulted claims on their merits.

Mr. Covington sought a certificate of appealability from the Sixth Circuit, the district court having declined to issue such a certificate. In December of 2002 — prior to the issuance of this court’s decision in Adams v. Holland — a judge of this court denied the application for a certificate. Adams v. Holland was decided in May of 2003, and on subsequent rehearing of the denial of the application a three-judge panel issued a certificate as to the eight ineffective-assistance subclaims that the district court had found to be procedurally defaulted. The decision to issue the certificate was based on Adams v. Holland. See Covington v. Mills, No. 02-5659, Order (6th Cir. Nov. 21, 2003).

II

As applied to the case at bar, Adams teaches that the subclaims in question should not have been dismissed on the ground that Mr. Covington failed to raise them before the Tennessee Supreme Court. Adams was based on Tennessee *665Supreme Court Rule 39, promulgated in 2001, which provides that

“[i]n all appeals from criminal convictions or post-conviction relief matters from and after July 1, 1967, a litigant shall not be required to petition for rehearing or to file an application for permission to appeal to the Supreme Court of Tennessee following an adverse decision of the Court of Criminal Appeals in order to be deemed to have exhausted all available state remedies respecting a claim of error.” Tenn. S.Ct. R. 39.

Because of Rule 39, our court concluded here in light of Adams, discretionary review in the Tennessee Supreme Court was not an “available” state remedy that had to be exhausted by Mr. Covington before he could seek federal habeas corpus relief.1 Our court held further that Rule 39 applies in federal habeas corpus cases that were filed, as this one was, before the rule was promulgated.

The state does not deny that under Adams the dismissal of the ineffective assistance claims on the ground that they had not been presented to the Tennessee Supreme Court was erroneous. But Adams, the state contends in a brief filed prior to the Supreme Court’s denial of ceHiorari in Adams, was itself wrongly decided.

The state’s argument cannot carry the day before our three-judge panel, as we are bound to follow prior published decisions of this court. See 6th Cir. R. 206(c) (“Reported panel opinions are binding on subsequent panels. Thus, no subsequent panel overrules a published opinion of a previous panel.”) If Adams is to be overruled, it will have to be by the full court sitting m banc.

Dismissal of the subclaims that were not presented to the Tennessee Supreme Court would be proper, notwithstanding Adams, if those subclaims were not presented to the Tennessee Court of Criminal Appeals either. See Tenn. S.Ct. R. 39 (“[W]hen the claim has been presented to the Court of Criminal Appeals or the Supreme Court, and relief has been denied, the litigant shall be deemed to have exhausted all available state remedies.... ”).

In the subclaims at issue here, Mr. Covington contends that his trial attorney failed to provide effective assistance in that he

(1) failed to request discovery,

(2) failed to investigate the case,

(3) failed to develop a coherent theory of defense,

(4) failed to seek expert assistance to enhance the quality of a tape recording that was received in evidence,

(5) failed to provide sound advice to Covington as to the exercise of his right to testify,

(6) failed to object to an improper jury instruction on reasonable doubt,

(7) failed to raise or preserve the issue of sufficiency of the evidence, and

(8) failed to object to a handwritten amendment of the indictment.

Of these subclaims, only numbers (2) and (4) — the attorney’s failure to investigate and his failure to seek expert assistance with respect to the tape recording— *666were discussed in the argument section of Mr. Covington’s brief to the Tennessee Court of Criminal Appeals. The fact section of the brief, however, described evidence showing that Mr. Covington had not agreed to the amendment of the indictment. The fact section further summarized evidence showing that the trial attorney had only talked to Mr. Covington about testifying a few minutes before Covington was called to the stand; that Covington had been under the impression that he was not going to testify; that he did not want to testify; and that the lawyer had not prepared him for testifying.

We think that these factual recitations, which appeared in a brief where ineffective assistance of counsel was raised as the sole ground for relief and which were “well within the mainstream of constitutional law,” fairly presented subclaims (5) and (8) to the state appellate court. See McMeans v. Brigano, 228 F.3d 674, 681 (6th Cir. 2000) (holding that a claim has been fairly presented to a state court “if the petitioner asserted both the factual and legal basis” for the claim).

Nothing relating to subclaims (1), (3), (6), and (7), on the other hand, was mentioned anywhere in the brief to the Tennessee Court of Criminal Appeals. Mr. Covington does not deny that he failed to raise subclaims (6) and (7). He argues that his claims with respect to failure to request discovery (subclaim (1)) and failure to develop a theory of defense (sub-claim (3)) were adequately raised by statements that his attorney “only filed one pre-trial motion which was a motion to suppress” and “did not spend a sufficient amount of time with [Covington] in preparing for the trial.” In our view, these statements did not fairly apprise the state appellate court of the specific factual bases for subclaims (1) and (3). Those claims were thus procedurally defaulted.

The state argues that this court should decide the merits of the non-defaulted sub-claims notwithstanding that the district court did not have occasion to address those issues. In our view, however, it would be preferable for the non-defaulted subclaims to be considered in the first instance by the district court. Accordingly, the judgment is AFFIRMED as to subclaims (1), (3), (6), and (7) and REVERSED as to subclaims (2), (4), (5), and (8), with the case being REMANDED for consideration of the latter on their merits.