We investigate the capacity and mutual information of a broadband fading channel consisting of a finite number of time-varying paths. We show that the capacity of the channel in the wideband limit is the same as that of a wideband Gaussian channel with the same average received power. However, the input signals needed to achieve the capacity must be “peaky” in time or frequency. In particular, we show that if white-like signals are used instead (as is common in spread-spectrum systems), the mutual information is inversely proportional to the number of resolvable paths L˜ with energy spread out, and in fact approaches 0 as the number of paths gets large. This is true even when the paths are assumed to be tracked perfectly at the receiver. A critical parameter L˜crit is defined in terms of system parameters to delineate the threshold on L over which such overspreading phenomenon occurs.