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Most people’s letters from PIs will say all this. That’s because the PI will usually consult the direct mentor for input (or have the direct mentor draft the LOR), or the applicant will have provided these details him/herself. PIs want to write strong, detailed letters for their good students.</p>
<p>And if you do request two recs from the same lab, redundancy is preferable to none. If the direct mentor’s letter is the source of important details, and the PI’s letter doesn’t corroborate those details, the direct mentor’s letter will be met with scepticism.</p>