We develop an automated wavelet-based spectral method for constructing an approximate confidence interval on the steady-state mean of a simulation output process. This procedure, called WASSP, determines a batch size and a warm-up period beyond which the computed batch means form an approximately stationary Gaussian process. Based on the log-smoothed-periodogram of the batch means, WASSP uses wavelets to estimate the batch means log-spectrum and ultimately the steady-state variance constant (SSVC) of the original (unbatched) process. WASSP combines the SSVC estimator with the grand average of the batch means in a sequential procedure for constructing a confidence-interval estimator of the steady-state mean that satisfies user-specified requirements on absolute or relative precision as well as coverage probability. An extensive performance evaluation provides evidence of WASSP's robustness in comparison with some other output analysis methods.