We consider systems of three spiking cells, driven by a common fluctuating input against independent background noise. The cells are chosen to be either simple sum-and-threshold units, linear integrate and fire, or nonlinear (fitted to spiking characteristics of retinal ganglion cells) integrate and fire. The inputs are chosen from distributions that are either gaussian, uniform, skewed, or bimodal. For each circuit, we compute the distribution on output spiking states either analytically or by sampling, approximate by a maximum entropy fit, and measure the goodness of fit via the Kullback-Leibler divergence between the two. We repeat over a range of input parameters: mean, total input variance, and the relative strength of common drive to background noise.