Orthogonal frequency-division multiplexing (OFDM) is a popular transmission format for emerging wireless communication systems, including satellite radio, various wireless local area network (LAN) standards, and digital broadcast television. Single-carrier cyclic-prefixed (SCCP) modulation is similar to OFDM, but with all frequency-domain operations performed at the receiver. Systems employing OFDM and SCCP perform well in the presence of multipath provided that the channel delay spread is shorter than the guard interval between transmitted blocks. If this condition is not met, a channel-shortening equalizer can be used to shorten the channel to the desired length. In modestly time-varying environments, an adaptive channel shortener is of interest. All existing adaptive channel shorteners require renormalization to restrain the channel shortener away from zero. In this paper, we study the use of a unit-tap constraint rather than a unit-norm constraint on the adaptive channel shortener. We use this constraint to manipulate existing algorithms into a framework analogous to the recursive least squares algorithm, and we develop adaptation rules for blind and semiblind frequency domain equalizers for SCCP receivers. Simulations of the proposed algorithms show an order of magnitude improvement in convergence speed, as well as a reduced asymptotic bit error rate.