The number of active users in code-division multiple access (CDMA) systems is often much lower than the spreading gain. The present paper exploits fruitfully this a priori information to improve performance of multiuser detectors. A lowactivity factor manifests itself in a sparse symbol vector with entries drawn from a finite alphabet that is augmented by the zero symbol to capture user inactivity. The non-equiprobable symbols of the augmented alphabet motivate a sparsity-exploiting maximum a posteriori probability (S-MAP) criterion, which is shown to yield a cost comprising the l2 least-squares error penalized by the p-th norm of the wanted symbol vector (p = 0, 1, 2). Related optimization problems appear in variable selection (shrinkage) schemes developed for linear regression, as well as in the emerging field of compressive sampling (CS). The contribution of this work to CDMA systems is a gamut of sparsity-embracing multiuser detectors trading off performance for complexity requirements. From the vantage point of CS and the least-absolute shrinkage selection operator (Lasso) spectrum of applications, the contribution amounts to sparsity-exploiting algorithms when the entries of the wanted signal vector adhere to finite-alphabet constraints.