In this paper we address the problem of suppression of a digital narrow-band interferer in direct-sequence spread spectrum (DSSS) communications, We focus on the adaptive suppression method proposed by Honig, Madhow, and Verdu [1] for wide-band interference, applying it to a narrow-band interferer, We identify the eigenspaces of the system dynamics to analyze the convergence of the adaptive version of the minimum mean square error (MMSE) algorithm for this application. Using this subspace approach we are able to: 1) significantly decrease convergence times via a new constraint on step size in adaptation; 2) introduce a simple parameterization of the mean output energy (MOE) and signal-to-interference ratio (SIR) to compare performance of various receivers; and 3) identify modes of operation where the algorithm will cease to effectively cancel interference. We propose a new adaptive receiver that avoids the convergence anomalies identified, while capitalizing on the new step size for faster convergence, Simulation results to support theoretical results are presented.