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In multicarrier systems with a cyclic prefix, interblock interference can be limited by shortening the channel impulse response using time-domain equalizers. In this paper, we present two blind channel-shortening algorithms that exploit the second-order statistics of the channel outputs. The equalizer parameter vector is chosen from a space that forces the length constraint on the effective channel impulse response. The first algorithm is less sensitive to channel-order estimation errors, whereas the second one is simpler to implement. Furthermore, we show that the two algorithms are equivalent for noiseless channels. Simulation examples are provided to demonstrate their superior performance over some existing algorithms.