Gregory Lawrence Moore, Texas prisoner # 799979, filed a petition under 28 U.S.C. § 2254 to attack his 1998 conviction and 20-year sentence for failure to appear. The district court granted relief on Moore’s claim that his appellate counsel had been ineffective for failing to timely notify Moore of the outcome of his appeal and the right to proceed further by filing a state petition for discretionary review (“PDR”). The district court denied relief on Moore’s remaining claims.

On the respondent’s appeal, this court vacated the judgment of the district court and concluded that the state habeas court’s denial of relief on Moore’s claim of ineffective assistance of appellate counsel “was *878 not contrary to or an unreasonable application of clearly established federal law as determined by the Supreme Court of the United States.” Moore v. Cockrell, 313 F.3d 880, 881 (5th Cir. 2002). This court remanded for further consideration in light of the deferential standard under the Anti-terrorism and Effective Death Penalty Act (AEDPA). Id. at 882.

On remand, the district court denied relief. Moore filed a timely notice of appeal and applied for a certificate of appeal-ability (COA). The district court granted COA on three issues raised for the first time in Moore’s COA application: 1) whether Moore had a constitutional right to file a state PDR; 2) who has the duty to timely inform a defendant of the outcome of his state direct appeal; and 3) whether there is a conflict between the Texas Rules of Appellate Procedure, the Federal Rules of Appellate Procedure, and this court’s decision in Moore.

In his brief, Moore attacks the rationale of the decision in Moore, arguing the three issues on which COA was granted. The respondent contends that this court should not consider Moore’s arguments because they were raised for the first time in his COA application in the district court.

In Roberts v. Cockrell, 319 F.3d 690, 695 (5th Cir. 2003), we stated that “[w]e generally will not consider a claim raised for the first time in a COA application.” We noted that the petitioner, who raised an equitable tolling argument for the first time in his COA application in the district court, “could and should” have raised the issue earlier. See id. Here, Moore had the opportunity to raise all of the issues on which COA was granted in his objections to the magistrate judge’s report, which recommended that his 28 U.S.C. § 2254 petition be denied based on the decision in Moore. Because Moore “could and should” have raised the issues prior to his COA application in the district court, this court will not consider them. See id. Accordingly, the judgment of the district court is AFFIRMED. The respondent’s motion to vacate the COA granted by the district court and to dismiss the appeal is DENIED.

After briefs were filed, Moore’s appointed counsel, John Bennett, moved to withdraw. The motion is GRANTED. See 5th Cir. Plan Under the Criminal Justice Act (“CJA”), § 5(B). David P. O’Neil is hereby appointed as his attorney. Moore’s motion is GRANTED. See 18 U.S.C. § 3006A(c); Fifth Circuit Plan under the CJA, § 3.