Synaptic vesicles are released stochastically, and therefore stimuli that increase a neuron's synaptic input might increase noise at its spike output. Indeed this appears true for neurons in primary visual cortex, where spike output variability increases with stimulus contrast. But in retinal ganglion cells, although intracellular recordings (with spikes blocked) showed that stronger stimuli increase membrane fluctuations, extracellular recordings showed that noise at the spike output is constant. Here we show that these seemingly paradoxical findings occur in the same cell and explain why. We made intracellular recordings from ganglion cells, in vitro, and presented periodic stimuli of various contrasts. For each stimulus cycle, we measured the response at the stimulus frequency (F1) for both membrane potential and spikes as well as the spike rate. The membrane and spike F1 response increased with contrast, but noise (SD) in the F1 responses and the spike rate was constant. We also measured membrane fluctuations (with spikes blocked) during the response depolarization and found that they did increase with contrast. However, increases in fluctuation amplitude were small relative to the depolarization (<10% at high contrast). A model based on estimated synaptic convergence, release rates, and membrane properties accounted for the relative magnitudes of fluctuations and depolarization. Furthermore, a cell's peak spike response preceded the peak depolarization, and therefore fluctuation amplitude peaked as the spike response declined. We conclude that two extremely general properties of a neuron, synaptic convergence and spike generation, combine to minimize the effects of membrane fluctuations on spiking.