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The Diversity Summer fellowships typically request 1L grades. Do the firms usually read applications on a rolling basis, or wait for the deadline?

Depends on your firm and your market. For example, my home/preferred market's biggest school doesn't give grades until the end of 1L year - making grades a moot point for many applicants. However, some firms will not pass along your application to the reviewing board until your grades are submitted. I don't think that it really made that big of a difference - I got callbacks from both (those who reviewed earlier and those that told me to reapply with my grades), but all of them where scheduled after second semester started. At least for my area, firms only take 1-2 1Ls, so they're not in a rush to make a final determination until they've looked at everyone.
Be sure to go to those 1L Diversity receptions over break if one is available where you'll be. You can ask the recruiters individually if you haven't already submitted your app. Good luck.

Also keep a look out for the smaller firms, who typically don't advertise for 1L positions until into February.