A lot of people anchor the palm muting side of their hand, in order to attempt to mute unplayed strings, but this causes problems:

* tendency to play with a lot of palm muting

* your resting pick position is above the strings, which means you have to lower it in order to pick a note (unnecessary motion)

* the muting isnt really that effective so you still get extra noise from the strings

I used to play just like this, trying to mute the strings with my palm. But I found a better way - you can just anchor the OTHER SIDE of your hand ...

Say you're playing on the D string...

1. Touch the high E string with your Pinkie
2. Touch the B string with your Ring finger
3. Touch the G string with your Middle finger
4. Touch the side of your THUMB to the low E and A strings to mute them.

Only the D string should have no fingers touching it.

This makes for great muting. You can scrape against the strings with your playing hand and only ONE string will play! That's powerful. Your pick position should be pretty much already touching the strings, so all you have to do to play a note is downstroke!

This is a really good technique, but may take time to develop.