In this paper, I argue, based on data from West Greenlandic, that languages can be truly tenseless, in the sense that their inflectional systems contain no node dedicated to the encoding of relations between speech time and reference time. My idea is that the burden of encoding temporal information actually falls mostly on the VP rather than on tense; so that true tenselessness entails neither a radical indeterminacy in the temporal interpretation of tenseless sentences nor a radically different description of the linguistic properties of tensed and tenseless languages, as some have claimed.