Watch the Picking Hand online guitar lesson by Brad Carlton from Guitar Lab: Super Sustain
This lesson focuses exclusively on picking hand dampening(or damping). This will involve a hybrid picking approach involving the pick, fingers, side of the thumb, and heel of the hand. Not only will this technique serve you in normal guitar playing, but if you ever decide to play slide guitar it will be indispensable in executing a clean sound.
I want to stress that I view techniques as tools in a huge rollaway toolbox. Each technique is available when needed which means you won't always use picking hand dampening. But if you have it when you need it you'll be glad you got it ingrained in your muscle memory.
Picking hand dampening also serves as a means of applying staccato to your notes which simplifies this issue in certain licks.