For the decoding of a binary block code of Hamming distance of d over AWGN channels, a soft-decision decoder is said to achieve bounded-distance (BD) decoding if its squared error-correction radius is equal to d. A Chase-3-like algorithm outputs the best (most likely) codeword in a list of candidates generated by a conventional algebraic binary decoder whose input sequences have nonzero entries confined in the most unreliable positions. Let η(d) denote the smallest size of input sequence sets of Chase-3-like algorithms which achieve BD decoding. In this paper, we show that there are positive numbers C 1 and C 2 such that C 1 ≤ η(d)d−1/2 ≤ C 2 for sufficiently large d.