Three Letters: At Least 3, or Only 3?

This issue came up in a side conversation in a previous thread, but I thought it warranted its own discussion. Anon 12:55 asks,

Letters of recommendation: they ask for 3. Sending 4 instead: always a bad idea, always a good idea, something in between? Elaboration appreciated.

And I said,

I always thought that the rule for letters is "as many as possible." I did a little research, and I don't think I know anybody who sends just 3. I was told that getting more and better letters, particularly from people who are not directly invested in your success, was one of the best things a candidate can do to improve her chances of nailing a job.

But anon 3:28 says,

I also heard the opposite advice -- they ask for 2, they want the strongest 2, and anything further would be diluting. that said, I always send (what I assume to be) the strongest x (2 or 3 have been small numbers I encountered recently) plus a teaching letter which I note in my cover letter is sent with that intent.

But I've never heard of that. Plus, I don't have any idea how to rank my letters from strongest to weakest. I've never read my letters. Plus, I'm not the one who sends them out. Plus, I don't even think there is even any provision in my Ph.D.-granting program's placement procedures for this sort of thing. And as if that wasn't enough, it would make the department secretary whose job it is to put these files together that much more involved. So I say, as many letters as possible is the right strategy.

--Mr. Zero