Despite the widespread use of up-down staircases in adaptive threshold estimation, their efficiency and usability in forced-choice experiments has been recently debated. In this study, simulation techniques were used to determine the small-sample convergence properties of stochastic approximation (SA) staircases as a function of several experimental parameters. We found that satisfying some general requirements (use of the accelerated SA algorithm, clear suprathreshold initial stimulus intensity, large initial step size) the convergence was accurate independently of the spread of the underlying psychometric function. SA staircases were also reliable for targeting percent-correct levels far from the midpoint of the psychometric function and performed better than classical up-down staircases with fixed step size. These results prompt the utilization of SA staircases in practical forced-choice estimation of sensory thresholds.