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The lidar crossover function f(R) in the lidar equation accounts for the incomplete overlap of the laser-pulse volume and the receiver field of view at short ranges and so is pertinent to near-surface returns from aerosols and precipitation. Using a Gaussian-intensity transverse profile for the laser pulse we present a comparatively simple formulation for f(R) and provide some numerical results for realistic lidar geometries, including the effects of optical axes misalignment. It is shown that for lidar systems constrained to narrow beam-widths (approximately 1 mrad) for polarization or other observations, accurate alignment is of great importance to lidar operations.