ABSTRACT: The authors perform discrete-mode calculations for a parametric amplifier with a quantum pump and discuss some of the limitations on calculations of this sort in quantum optics. They calculate corrections to the squeezing due to quantum fluctuations to order N^-2, for a pump initially in a coherent state with average photon number N. The authors find that the limit to the variance of the squeezed quadrature due to the quantum nature of the pump goes as N^-1/2.