The Wiener diffusion model with two absorbing barriers is often used to describe response times and error probabilities in two-choice decisions. Different representations exist for the density and cumulative distribution of first-passage times, all including infinite series, but with different convergence for small and large times. We present a method that controls the approximation error of the small-time representation that occurs due to finite truncation of these series. Our approach improves and simplifies related work by Navarro and Fuss (2009) and Blurton et al. (2012, both in the Journal of Mathematical Psychology).