We consider prefiltering for a single-carrier transmission over frequency-selective channels, where reduced-state trellis-based equalization is employed at the receiver, such as delayed decision-feedback sequence estimation (DDFSE) or reduced-state sequence estimation (RSSE). While previously proposed prefiltering schemes are based on the optimum filters of decision-feedback equalization (DFE), the prefiltering scheme introduced in this paper is designed according to a signal- to-interference-plus-noise ratio (SINR), whose definition takes into account explicitely the subsequent trellis-based equalizer and its complexity. In addition to the prefilter, a finite-length target impulse response for DDFSE/RSSE and an infinite- length feedback filter for state-dependent decision feedback in DDFSE/RSSE, respectively, is optimized. The developed solutions lend themselves to an interpretation of the tasks of the optimum filters. The presented numerical results show that noticeable gains can be achieved compared to state-of-the-art prefilters.