I was recently attempting to switch out brakes on a beater mountain bike, and ended up shearing one of the bolts right at the base of the head. The bolt was almost completely in, and it felt like it was threading normally, though it must not have been (unless the bolt was defective--it was also off of an old bike). Either way, it left me nothing to grab on to above the brake post.

I've searched around with no real luck concerning getting that bolt out or re-threading the brake posts. Anyone ever come across this, or know any tricks? It seems that taps and re-threading devices are quite temperamental and require "ideal" conditions to work well. Any info or advice would be welcome.