As always, I agree with CnH to most extents...
As an applicant, it's tempting to go with big names, however as we residents were reviewing applications this year, I found that some uppers found it was very obvious that some "big named textbook author" letters were useless carbon-copies and were, are such, disregarded. Double-minus points if the author referred to the applicant in the wrong gender...
Yet, I'm sure that many of my letters from last year (by more-modest unknown folks) were also generally disregarded.
There's probably some balance here, and that having a sponsor known to the folks to whom you're applying is very useful. For the random program, maybe having a variety of letters all highly supportive may also be useful. One of my letters was from a GP, another was from a general surgeon, and both were parts of applications which ended up getting interviews.
In the end, 3 COMPLETE STRONG letters may be better than 2-good and 1-disregarded letter... though this may not be as good as 1 well-known-to-the-program-and-may-call-to-say-so letter (although you have to be honest that this doesn't happen as often as you'd think... most folks simply aren't worth the effort or aren't that special).
The moral is: get the best letters you can from every surgeon you respect (many let you read and/or write their letters no matter what the waiver says) and APPLY BROADLY. Let me repeat again: APPLY BROADLY.