The discrete angle technique is a customary method for selecting scattering angles from such scattering laws that are given through their Legendre coefficients up to some finite order. In this technique, discrete scattering angles are selected with certain probabilities. In low-order Pn truncations, however, this method can lead to unwanted ray effects during the first few free flights of the random walk. We propose a method in which a linear combination of some arbitrary density function, having the same first 2n moments as the truncated expansion, and of a discrete density function will yield samples that conserve the first (2n + 2) moments of the truncated series. Bounds are derived on the possible ranges of the combination coefficient. The method is applied to construct a semicontinuous density function (continuous + Dirac delta functions) having the first four moments prescribed, i.e., being given by its first three Legendre coefficients.