In this article, we describe two new programs that compute both p-values and confidence intervals (CI) for the indirect effect in mediational models, including a) a p-value based on the partial posterior method, which we refer to as p3 computed across the posterior distribution of the regression coefficients; b) a variant of p3 that uses a normal approximation for the posterior distributions, p3N; c) Hierarchical Bayesian CIs (CIHB) based on the posterior distributions of the regression coefficients; and d) CIs based on the Monte Carlo method (CIMC). These programs do not require access to raw data as do resampling methods. Similar to Sobel’s test, p3 and p3N constitute a single p-value for the indirect effect while performing substantially better in terms of Type I and II error rates. Furthermore, we include a memory efficient computational algorithm for CIHB and CIMC that allows for precision beyond that in existing alternative implementations. The underlying programs can utilize multicore processors, and their performance is tested through a simulation study. Finally, the use of these programs is illustrated with an empirical example.