Originally Posted by FBinNY

Brake squeal ultimately is the result of lack of rigidity in the brakes. As you apply the brakes the rim's forward motion pushes the shoes forward. Since the pivots are back from the braking surface, this cause the pads to rotate slightly, bringing the toes out and heels in. When the shoes can't move forward any more and a more slippery area of the rim comes along the pad slips back to the original position. This happens at high speed causing a vibration which can be felt as a shuddering, or heard as a squeal.

This only happens at moderate braking pressure because as you brake harder, the shoes are forced flat to the rim and cannot rotate.

The cure is to clean the rim and shoe surface so the braking action is more uniform. Toe-in helps up to a point when it's done so the rotating motion brings the shoe flat at moderate braking force. Otherwise, anything you can do to increase overall rigidity helps. Adding a shim to eliminate any free play of the brake on the post, using a stiff grease between the bushing and post.

Long heeled posts (Kool Stop design) help because they resist the rotation. In very tough cases I've had some success filing away the rear corner of the shoe into a ski tip so there wouldn't be a corner to dig in as the pad rotated, but this has the drawback of worsening wet performance, ad does excess toe-in.

FWIW, my canti commuter has brake squeal when it's humid, but it clears up within a day or two. In the meantime I think of it as an automatic horn which isn't all that bad in city traffic.

If all else fails and the squealing is really bothering you, a brake booster horseshoe can do a great job curing it.