Summary: The nonparametric Bayesian shape-constrained bioassay estimator of P. Ramgopal et al. [Biometrika 80, No. 3, 489-498 (1993; Zbl 0787.62115)] is compared with the shape constrained maximum likelihood estimator through simulations. The purpose is to illustrate that, in the absence of prior information other than the shape constraints, the less computationally intensive MLE might be an acceptable alternative. Data are simulated from an underlying potency function and both estimates are computed with the assumption that the shape is known (either concave or convex-concave, both nondecreasing over the support). Several different sampling functions and sample sizes are chosen to investigate the behavior of the estimators in varying conditions. An efficient algorithm for computing the shape-constrained MLE is presented. A theorem provides the theoretical justification for this new algorithm.