Sparse equalizers, in which only a small subset of the filter taps is selected to be nonzero, were recently proposed as a low-complexity solution for receivers operating in wireless frequency-selective channels with sparse power profiles. The performance of the sparse equalizer heavily depends on its tap-positioning algorithm. This paper presents efficient low-complexity algorithms for determination of sparse equalizer tap positions based on a forward sequential search. We develop low-complexity metrics for the evaluation of the candidate tap positions in the search space as well as methods to effectively reduce the search space size. The proposed algorithms are shown to be superior over previously proposed algorithms in a wide range of channel conditions. Actually, the proposed algorithms yield, in most of the tested cases, performance identical to the optimal, prohibitively complex, tap-positioning algorithm. The main emphasis is on linear equalization suitable for wideband code-division multiple-access systems but the algorithm can be extended to a variety of equalization schemes and channels.