Create random number within an annulus

I am trying generate a random number that is within an annulus, i.e. we have a max and min radius. I tried doing:

while True:
    x=random.uniform(-maxR, maxR)
    y=random.uniform(-maxR, maxR)
    R=math.sqrt(x**2 + y**2)
    if R <= maxRadius and R >= minRadius:
        if x>= -maxRadius and x <= maxRadius and x<=-minRadius and x>= minRadius:
            print "passed x"
            if y>= -maxRadius and y <= maxRadius and y<=-minRadius and y>= minRadius: 
                break

But this is very slow. Is it possible to feed more contraints into random.uniform or is there another method?