In earlier work, a stochastic method for reconstructing certain classes of two-dimensional binary images from limited projection directions was presented. In the present study, we experiment with different implementations of this method to minimize the running time. Our fastest implementation is based on a look-up table and pre-generated arrays of random integers. This is more than 40 times faster than the implementation used in the earlier work. This speedup makes it practical to conduct extensive searches to find the optimal values of the method's parameters for each class of images to be reconstructed.