KEARSE, Circuit Judge.

These 16 appeals are pursued by 14 New York State ("State") prisoners whose petitions for writs of habeas corpus under 28 U.S.C. § 2254 were denied in orders of the United States District Court for the Eastern District of New York adopting the reasons stated by the State appellate court in affirming the respective petitioners' convictions and the reasons proffered by the State in opposing the habeas petitions. The appeals were consolidated by order of a prior panel of this Court dated May 4, 2000. Limited certificates of appealability were granted by that panel, and counsel was appointed to address, for all of these petitioners, the following question:

whether a district court may dismiss a 28 U.S.C. § 2254 petition without providing an order which indicates that the court conducted a thorough review and independent analysis of the petition.

After briefing by appointed counsel and the State, the appeals were argued before the present panel in June 2001. In Rudenko v. Costello, 286 F.3d 51 (2d Cir. 2002), we noted the language of the limited certificates of appealability, see id. at 61; but we "presume[d] that the district judge[s] ha[d] given each matter personal attention," id. at 67, and we thus addressed only a different question, to wit, whether "the district courts are required to render decisions that are at least sufficiently informative to permit meaningful appellate review," id. at 64; see also id. at 57, 65, 80-81.

The phrasing of the certificates of appealability, however, unfortunately gave some the impression that this Court believed that district judges were not giving thorough reviews to or conducting independent analyses of habeas petitions. That impression was erroneous. We had no intent to convey such a thought or to suggest that the judges were not deciding such cases responsibly, and we hereby withdraw the inappropriately phrased May 4, 2000 certificates of appealability. The opinion filed in Rudenko v. Costello, 286 F.3d 51, is also withdrawn.

This vacatur of the certificates of appealability revives the question, in each of these cases, as to whether the application for a certificate of appealability should be granted, i.e., whether the applicant has sufficiently made "a substantial showing of the denial of a constitutional right," 28 U.S.C. § 2253(c), to permit an appeal. As these cases involve petitioners who, in 16 separate prosecutions, were convicted of a variety of crimes that were apparently unrelated, each application will require particularized consideration. We thus conclude that consideration of these applications as a group serves no useful purpose, and we therefore vacate the May 4, 2000 order of consolidation as well.

As discussed in opinions we file today in Miranda v. Bennett, 322 F.3d 171 (2d Cir. 2003), and Gandarilla v. Artuz, 322 F.3d 182 (2d Cir. 2003), we conclude that in some cases a district court's adoption of the opinions of the state appellate court and of the State's contentions opposing the respective habeas petitions does not provide this Court with sufficient information to conduct a meaningful appellate review or to determine whether a certificate of appealability is warranted. We think it clear that greater specificity is needed in Miranda v. Bennett and Gandarilla v. Artuz, and in those cases we remand to the district court for identification of the ground or grounds on which those petitions, or certain claims asserted in them, were rejected.

The need for greater specificity in the remaining 14 cases is less plain. Although it is not clear from the district court's orders that the petitions were rejected for lack of merit, an evaluation of the merits by this Court may reveal that, regardless of the ground of decision, a given petitioner has not made a substantial showing of the denial of a constitutional right. We leave the applications for certificates of appealability in those cases for consideration by other panels in due course, after further processing of those applications by this Court's staff.