Echo-location systems are unavoidably subject to range-velocity ambiguities. Although the total amount (volume) of ambiguity increases with increasing signal bandwidth, it is shown here that ambiguity density decreases with increasing bandwidth. This result, which is stated in the paper as a theorem, means that for systems observing targets with restricted relative velocities, the effective volume of ambiguity decreases as the bandwidth is increased. It is suggested that this may help one to understand the performance of mammals with advanced echo-location senses, since increasing the bandwidth not only reduces effective ambiguity volume but also improves range resolution and reverberation suppression. For a given bandwidth the effective ambiguity volume is minimized if the energy spectrum of the echo-location signal is uniform throughout the band.