A few years back, the Federal Rules of Appellate Procedure gave amici in the Courts of Appeals 7 days after the party supported to file their briefs, instead of the prior rule of contemporaneous filing. Two years ago, the Supreme Court adopted the 7-day lag at the suggestion of yours truly.

Does the 7-day lag apply to amici supporting rehearing en banc in the Court of Appeals? No, says Judge Easterbrook in this in-chambers opinion (h/t, How Appealing), shooting down AARP's attempt to file in a pension case. For rehearing petitions in the CA, amici are still subject to the contemporaneous filing requirement.

So when can you file an amicus in support of rehearing in the Supreme Court? Never. See Sup. Ct. Rule 37.3(a).