Due to the scarcity of frequency allocations for emerging personal communications services, it has been proposed that spread spectrum (SS) signals be used in such services so that they can be overlaid on existing frequency band occupants. Such SS signals would be constrained in power so as not to interfere with pre-existing, narrowband users. In view of this application, suppression of strong narrowband signals that interfere with commercial SS communications systems is being investigated with renewed interest. Previous research has modeled the narrow-band user as a sinusoidal or autoregressive signal, and consequently has advocated use of predictive filtering to suppress the narrowband signal. In this paper it is shown that when the narrowband interferer is in fact a digital communications signal that these methods are less effective than techniques derived from multiuser communications. In particular, by modelling a narrowband user as a digital signal, optimal and asymptotically (low background noise) optimal linear algorithms for the recovery of the SS bit stream are developed. This technique represents not only a promising new approach to narrowband interference suppression, but also a new application for multiuser detection theory.