Simultaneous Painting problem

I am programming a game where I have

i) map
ii) mini-map
iii) Unitpanel (with info about units and stuff).

I have problems when several of them want to repaint simultaneously.

I have noticed that I only get a smooth, even and not intruded painting when I only let i) paint becaue if I let ii) and iii) paint then I sometimes get graphics flashing by in the wrong places (apparently because of simultaneous painting) and some temporary choppyness.

Since there are loads of solution I will name a few of them for you to recommend me to do and perhaps you find one that is not even on my list

solution:
a) Making some kinf of thread safe repainting on ii) and iii) so that they do not paint while map is painting (synchronized java keyword) ?
or
b) using some kind of priority by combining paintimmediately, repaint(long millis) or other methods

by the way, I use JRE1.42 and I use Swing and JPanels for everything where I want to paint.