I found some pieces recently I would like to learn with tremolo passages, but I've never had a good tremolo in spite of years of attempting various techniques for working on it. My new theory is that I need to develop the weaker side of my hand, and I've come up with a good way to work on that which is working great so far.
The first set of exercises begins with playing 1-2-3-4 with the left hand. Starting on the 6th string at the first fret, 1-2-3-4, repeat on the 5th string, 4th, 3rd, 2nd, 1st, then up a fret and back across string by string to the 6th. Repeat this pattern all the way up the neck until you have the 4th finger at the 1st string 12th fret. From there, the pattern is reversed, descending 4-3-2-1 and descending back down the neck the same way it was climbed. You should end with the 1st finger on the first fret on the 6th string again. This is a fairly standard pattern of exercise which most will recognize right away.
The right hand fingering with this is a strictly repeated a-m-i the whole way. So beginning on the 6th strings, you'll play a-m-i-a, then on the 5th, m-i-a-m, i-a-m-i on the 4th, etc. I do this all with light rest strokes to keep the motions small and precise. If you're like me, you'll probably find that it becomes more difficult to coordinate this on the way back down the neck when the left hand pattern is reversed. I think this is because the brain will at first decide that both hands are playing the same pattern, and you will need to do the exercise slowly enough to gently and carefully convince your mind that the patterns are in fact separate. As this becomes comfortable, you can use different left-hand patterns... 1-3-2-4 ascending with 4-2-3-1 descending, 1423/3241, 1432/2341, etc.
The first exercise doesn't have to be completely mastered before going on but I think it's worth developing that for a while first. The next exercise uses exactly the same left hand fingerings as the first, but the right hand uses p-a-m-i for each group of four for the entire exercise. As that become comfortable, try (again with the same left hand pattern) using a-m-i-p for each group of four, then m-i-p-a and finally i-p-a-m. This will present tricky string crossings which will take a while to master.
The next step along the way is to practice scales using these same right-hand fingering patterns. This will again make for a variety of tricky string crossings and it will take some time to get comfortable with them. I begin with the standard "Segovia" fingerings for the scales and then progress from there, perhaps as follows although I think that there will be diminishing returns when it comes to spending a lot of time progressing through similar patterns.
i-m
m-i
i-a
a-i
m-a
a-m
a-m-i
m-i-a
i-a-m
i-m-a
m-a-i
a-i-m
i-m-a-m
m-a-m-i
a-m-i-m
m-i-m-a
p-a-m-i
a-m-i-p
m-i-p-a
i-p-a-m
As you go through these exercises, periodically try some simple tremolo exercises to see how you are progressing. I've come to believe a sentiment expressed by teacher Paul Croft on the Delcamp.net classical guitar forum, essentially that good tremolo follows from good right hand technique. I don't mean to say you shouldn't practice tremolo on its own, but the exercises I've presented above are designed to develop the kinds of coordination and concentration that will help build that balanced right hand technique. I have personally made quicker progress by practicing this regimen than I had by practicing Giuliani arpeggios and tremolo in isolation.
One last thing I want mention is that a lot of us succumb to the temptation to mainly use p, i, and m for most of our music. Indeed, a lot guitar music particularly in the early stages is playable without making substantial use of a. I think it is worth fingering pieces so that a is used as frequently as m and i, if possible. Even if it is not necessary to the piece, it will be a great benefit to one's technique overall.
This post owes a debt of gratitude to Alice Artzt's book, "The Art of Practicing." In it, she describes more or less the same kinds of exercises, and a system for devising many more along the same lines. The exercises I presented here are inspired by her method and are ones that have been working well for me so far.