Bayesian optimal inference is often heralded as a principled, general framework for human perception. However, optimal inference requires integration over all possible world states, which quickly becomes intractable in complex real-world settings. Additionally, deviations from optimal inference have been observed in human decisions. As a candidate alternative framework to address these issues, we propose point estimate observers, which evaluate only a single best estimate of the world state per response category. We compare the predicted behavior of these model observers to human decisions in five perceptual categorisation tasks. Compared to the Bayesian observer, the point estimate observer loses decisively in one task, ties in two and wins in two tasks. Thus, the point estimate observer is competitive with the Bayesian observer and should be considered in future model development and experimental studies.