Practice alternate picking with chromatic scale patterns, and try to pick all notes when you play arpeggios (assuming that you sweep them instead of picking them note to note)
And ofcourse, tremolo excersises are great when you want to improve your right hand technique but try them for example like this:
D----------------------------------------12-12-12-12
A---------------------12-12-12-12
E-12-12-12-12-
and so on..
And ofourse in triplets as well because when you pick alternating you must pick every string from a different direction.
Hopefully that's any help.. :)
"If practise makes perfect, and no one is perfect, why practise? Duh.."
