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Chase decoders permit flexible use of reliability information in algebraic decoding algorithms for error-correcting block codes of Hamming distance d. The least complex version of the original Chase algorithms uses roughly d/2 trials of a conventional binary decoder, after which the best decoding result is selected as the final output. On certain channels, this approach achieves asymptotically the same performance as maximum-likelihood (ML) decoding. In this correspondence, the performance of Chase-like decoders with even less trials is studied. Most strikingly, it turns out that asymptotically optimal performance can be achieved by a version which uses only about d/4 trials.