Muted slap notes

[CaseLogic]

I've been playing bass for almost 4 years, but sadly I have hardly practiced any slap bass. Even though the styles I like to play don't have much slap, it's good to add it to my bag of tricks.

When I play slap, I think I've formed a bad habit of resting my thumb on the E or A string when I go to pop the octave. For example, take the following:

D--------5
A---------
E-3--x----

When I hit the mute, rather than use my left hand to mute the string and slap normally, I do a form of right hand mute. What I do is I slap, but don't rebound so the note can't resonate and essentially I get the percussive sound that way. With my thumb resting on the lower string, I use that as leverage to pop.

Are right-hand muted slaps like that even proper technique? Or did I just pull that out of my ass?

The problem is, if I have something like this:
D--------5
A---------
E-3--3----

I have the habit of muting that last 3 like above.

Should I stick solely with left hand mutes?

edit: Also, what are some good songs to practice slap bass that AREN'T RHCP? Out of the music I listen to, RHCP has the most slap bass so I'd like to pick up something new. Any genre is fine, I'm trying to expand anyways =)

[CaseLogic]

I was hoping to get some opinions and advice

[tswd]

I do the same thing that you do, I think. I'll tend to palm mute with my right hand for the dead notes. For example, if you have something like this

D --3h5-
A ------
E X-----

I find it easier to mute with the right for the dead note while the left hand gets ready for the hammer-on. If I want the E string to ring out, I just lift my palm off the string.

As far as songs, I can't really recommend any specifically. I learned to slap from Tony Oppenheim's book. I'd highly recommend getting it and forcing yourself to work through all the lessons. It's amazing how much is actually in that book.