We propose that word recognition in continuous speech is subject to constraints on what may constitute a viable word of the language. This Possible-Word Constraint (PWC) reduces activation of candidate words if their recognition would imply word status for adjacent input which could not be a word--for instance, a single consonant. In two word-spotting experiments, listeners found it much harder to detect apple, for example, in fapple (where [f] alone would be an impossible word), than in vuffapple (where vuff could be a word of English). We demonstrate that the PWC can readily be implemented in a competition-based model of continuous speech recognition, as a constraint on the process of competition between candidate words; where a stretch of speech between a candidate word and a (known or likely) word boundary is not a possible word, activation of the candidate word is reduced. This implementation accurately simulates both the present results and data from a range of earlier studies of speech segmentation.