Solidify modifier creating protrusions though adjacent faces

I apologize if this is an obvious issue of user error (which I’m sure it is). I’m trying to apply the solidify modifier to a model and when I do, some areas result in protrusions through exterior faces. Typically this is occurring, I believe, where faces intersect at acute angles and where the piece is thinner than the thickness value in the modifier.

I tried some of the other options in the modifier, and while the clamps option eliminated this issue, it also reduced the effective thickness of the modifier.

Any help is greatly appreciated. Below is a comparison view of a portion of the model without/with the solidify modifier visible. Please let me know if there’s additional information that I should provide.

https://farm1.staticflickr.com/567/22948017709_d382ee5d2d.jpg

If you want to have different thicknesses created with the solidify modifier use weight paint those areas to give less effect from the modifier. Then add that vertex groups to the modifier panel
https://www.blender.org/manual/modeling/modifiers/generate/solidify.html