In mobile radio, fading-envelope prediction can improve the performance of adaptive modulation techniques that require up-to-date channel-state information for optimal performance. We show how to compute the minimum mean squared prediction error of a mobile-radio fading envelope modeled as a stationary, bandlimited process arising from a diffuse set of local scatterers. For bandlimited processes, it is difficult to solve for the Wiener predictor using the usual spectral-factorization approach. Our method reduces the prediction problem to an eigenvalue decomposition, and is appropriate when the prediction is to be based on error-corrupted estimates of a narrowband fading process. We also show how to bound the error in the computation due to truncation of infinite series.