Perfectivity is often assumed to entail the completion of the event described by eventdenoting stems and their arguments. Although some scholars have noted that perfective markers do not always entail completion, their formal definitions contradict their informal descriptions. We show that these traditional models of perfective aspect cannot account for the aspectual system of Thai. In Thai, perfective markers do not entail that the event was completed: the resulting state of sentences that are in appareance telic in their 'inner aspect' need not have been reached. We call these non-completive perfective markers semiperfectives. We propose a formal model of semi-perfectivity within Discourse Representation Theory that relies on the inclusion of an imperfective operator in the lexical meaning of Thai accomplishment verbs as well as the notion of maximal event relative to an event description. We show that this latter notion is strictly weaker than the traditional notion of telicity, thus demonstrating that (a)telicity is not the sole property of event descriptions relevant to the semantics of grammatical aspect.