Numerical solution of the Bayesian recursive relations by the point-mass approach is treated. The stress is laid on the grid design as the main user design problem in this approach. An anticipative approach for finding a minimum sufficient number of grid points is developed, yielding a new adaptive algorithm reducing the computational operations without a loss of estimation accuracy. A numerical example is presented to compare the new algorithm with the standard point-mass technique and with a sequential importance sampling nonlinear filtering algorithm.