A constrained least-mean-square (LMS) technique that utilizes a modified optimality criterion which enhances the detection capabilities of direct-sequence spread-spectrum systems is presented. Two transversal tapped delay lines (TDLs) are operated simultaneously, one containing the received data and the other containing the constraint data. One set of adaptive weights operates on both TDLs with the LMS algorithm as the update technique. The filter weights are updated with respect to both minimizing the mean-square output error and minimizing the constraint error. Two types of constraint conditions are considered. The first is a correlation-matching condition and the second is a minimum-filter-energy condition. Simulation results presented demonstrate the output mean-square error improvement obtained by using the constrained rejection filter.