While the verification of security protocols has been proved to be undecidable in general, several approaches use simplifying hypotheses in order to obtain decidability for interesting subclasses. Amongst the most common is type abstraction, i.e. considering only well-typed runs of the protocol, therefore bounding message length. In this paper, we show how to get message boundedness “for free” under a reasonable (syntactic) assumption on protocols, in order to verify a variety of interesting security properties including secrecy and several authentication properties. This enables us to improve existing decidability results by restricting the search space for attacks.