A letter from your post doc is kind of like a letter from your 4th grade girlfriend saying what a great kisser you are. get real
a letter from the PI, even if totally fake is what you want. LOR's are fake and barely read, unless the person reading the letter personally knows the writer, in which case, if you are worth a crap, that person would have already placed a phone call on your behalf
Repeat :
letters from the guy that cuts your lawn, other students, your Mom, your mailman, residents, fellows, your best friend, and Post Docs are
worthless
one other thing :
DO NOT get a LOR from somebody that does not give good LOR's.
People on ad coms read dozens of LOR's You are nothing special to them, just a number. They couldn't care less about you or your LOR.
BUT a letter that is poorly written, has red flags in it ( real or unde cover) or flat out does not recommend you will place your application into the crapper.
LOR's can hurt more than they can help.
Between you me and a hole in the wall, i functioned for a year on a specific ad com, and at the weekly meeting for a year reviewing applications, I learned a thing or two about this topic. Saw a lot of BAD applications. Some of you are down right pathetic!
your post doc can write the letter for the PI and have the PI sign it. whatever, just get the big cheese to do your letter. Hell, you can write it for the post doc.
Make yourself out to be some kind of hero.
Lie through your teeth. It will prepare you for a career in medicine, more than you will ever know.
and God forbid whatever you do, don't have some TA do your letter. They usually have Napolean complexes and go out of their way to feel self important and practically beg to write your letter.
Tell them you want a letter from somebody that doesn't have the word assistant in their title cuz if I'm reading your file and I see the letter from some TA, I'm going to go excuse myself and heave a Havana and use their letter for TP