The "EJ" ensemble (i.e., ensemble with fixed total energy and angular momentum) momentum sampling algorithm recently proposed by Nyman et al. [J. Chem. Phys. 93, 6767 (1990)] is verified to give correctly distributed atomic momenta. The proof is based on explicit analytic determination of the atomic momentum distribution generated by the algorithm. The simpler case of microcanonical momentum sampling is also treated using similar methodology.