The sensitivity of the equatorial stratospheric climate to variations in the gravity wave parameterization is examined in the Unified Model. Particular emphasis is placed on the response of the annual cycle and quasi-biennial oscillation of zonal winds. Two classes of variations are considered. The first consists of variations in the source strength of the classic deterministic formulation of a Doppler-spread Doppler-shifted gravity wave scheme. The second consists of variations in the probability density function of the source strength parameter in a stochastic formulation of the same scheme. The effects on stratospheric climate of variations in the source strength of a deterministic scheme can be predicted from theory. In such a scheme, when choosing the best possible value for the source strength, a trade-off between a proper representation of the quasi-biennial oscillation and the annual cycle is inevitable. Implementation of a stochastic source strength in the resident gravity wave scheme is justified by the need to better represent the intermittent nature of the convective generation of gravity waves. The most striking effect of the stochastic parameterization is the stabilization of the quasi-biennial oscillation in multidecadal simulations. We suggest that this is due to the ability of the stochastic gravity wave parameterization to deposit a larger portion of gravity wave drag in the middle stratosphere.