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Is it counted against you to say you do not want to consider doing a summer term in your application?

I would want to do the summer start, BUT I'm applying directly out of undergrad and I can't imagine finishing my senior thesis only to start law school the very next week. Will the adcomm see my application and infer that this is the reason or will they think I'm not as serious about the school?

They usually try not to put people that are still in school in the Summer Term class anyway. You should be fine saying you don't want it.