Some alternatives for simple importance sampling [compare Kloek and van Dijk (1978) and van Dijk and Kloek (1980)] are investigated for the compu— tation of posterior moments and densities. An importance sampling method that is based on a mixture of a finite number of multivariate normal densities is compared with simple importance sampling and with a method that is based on a combination of Monte Carlo and classical numerical integration. These methods are intended to handle econometric applications where a simple importance function that is a reasonable approximation to the posterior density is difficult to find. For illustrative purposes use is made of a small econometric model. The results include bivariate marginal densities of the importance functions and the posterior plotted in three dimensional figures.