  We present an efficient method to solve Schr\"odinger's equation for
perturbations of low rank. In particular, the method allows to calculate the
level counting function with very little numerical effort. To illustrate the
power of the method, we calculate the number variance for two pseudointegrable
quantum billiards: the barrier billiard and the right triangle billiard
(smallest angle $\pi/5$). In this way, we obtain precise estimates for the
level compressibility in the semiclassical (high energy) limit. In both cases,
our results confirm recent theoretical predictions, based on periodic orbit
summation.
