Monte Carlo simulations are widely used to study the transmission and scattering of gamma rays. Use of this method for simulations of emission tomographs suffers from geometric inefficiency resulting from the low solid angle of acceptance of most tomograph designs. We have applied several importance sampling techniques--stratification, forced detection, and weight control through Russian roulette and splitting--to increase the computational efficiency of the Monte Carlo method 10- to 300-fold. A description of these techniques, their validation, and sample performance results are given. Application of importance sampling methods makes it practical to study photon scattering in heterogeneous attenuators on workstations and minicomputers.