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The Levenshtein’s channel model for substitution errors is relevant in information retrieval where information is received through many noisy channels. In each of the channels there can occur at most t errors and the decoder tries to recover the information with the aid of the channel outputs. Recently, Yaakobi and Bruck considered the problem where the decoder provides a list instead of a unique output. If the underlying code C ⊆ F2n has error-correcting capability e, we write t = e + ℓ, (ℓ ≥ 1). In this paper, we provide new (constant) bounds on the size of the list. In particular, we give using the Sauer-Shelah lemma the upper bound ℓ + 1 on the list size for large enough n provided that we have a sufficient number of channels. We also show that the bound ℓ + 1 is the best possible. Most of our other new results rely on constant weight codes. [ABSTRACT FROM AUTHOR]