GUEST said this: You can make a beautiful Eb by playing the C position @ 4th fret and mute the high E.

Rather than muting the high E string, why not drop the little finger onto it at the 6th fret and add the Bb note missing from the above?

frankie said this: Guests' position for an Eb above is a good one but you want to mute the G string as well with your middle finger and you can also reach over the top with your thumb and put a Bb in the bass (6th string, 6th fret).

Why bother muting the G string, since G is a note in the chord, and in fact is the note fingered on the D string?