In one-shot experiments, units are subjected to varying levels of stimulus and their binary response (go/no-go) is recorded. Experimental data is used to estimate the “sensitivity function”, which characterizes the probability of a “go” for a given level of stimulus. We review the current GLM approaches to modeling and inference, and identify some deficiencies. To address these, we propose a novel Bayesian approach using an adjustable number of cubic splines, with physically-plausible smoothness, monotonicity, and tail constraints introduced through the prior distribution on the coefficients. Our approach runs “out of the box,” and in roughly the same time as the GLM approaches. We illustrate with two contrasting datasets, and show that our more flexible Bayesian approach gives different inferences to the GLM approaches for both the sensitivity function and its inverse.