Computation in the nervous system often relies on the integration of signals from parallel circuits with different functional properties. Correlated noise in these inputs can, in principle, have diverse and dramatic effects on the reliability of the resulting computations. Such theoretical predictions have rarely been tested experimentally because of a scarcity of preparations that permit measurement of both the covariation of a neuron's input signals and the effect on a cell's output of manipulating such covariation. Here we introduce a method to measure covariation of the excitatory and inhibitory inputs a cell receives. This method revealed strong correlated noise in the inputs to two types of retinal ganglion cell. Eliminating correlated noise without changing other input properties substantially decreased the accuracy with which a cell's spike outputs encoded light inputs. Thus, covariation of excitatory and inhibitory inputs can be a critical determinant of the reliability of neural coding and computation.