In neural integrators, transient inputs are accumulated into persistent firing rates that are a neural correlate of short-term memory. Integrators often contain two opposing cell populations that increase and decrease sustained firing as a stored parameter value rises. A leading hypothesis for the mechanism of persistence is positive feedback through mutual inhibition between these opposing populations. We tested predictions of this hypothesis in the goldfish oculomotor velocity-to-position integrator by measuring the eye position and firing rates of one population, while pharmacologically silencing the opposing one. In complementary experiments, we measured responses in a partially silenced single population. Contrary to predictions, induced drifts in neural firing were limited to half of the oculomotor range. We built network models with synaptic-input thresholds to demonstrate a new hypothesis suggested by these data: mutual inhibition between the populations does not provide positive feedback in support of integration, but rather coordinates persistent activity intrinsic to each population.