The Aspect Hypothesis assumes that--in early interlanguages--the perfective past spreads from telic to atelic verbs because events occurring in the past are easier to be associated with predicates having an inherent endpoint in their lexico-conceptual representation. In this study it is questioned whether for initial L2ers knowing the general meaning of a verb entails knowing also its actional template and that learners have innate principles that drive them to distinguish telic and atelic verbs from scratch. Data from our experiment of prompted narrative suggest that L1 English, L2 Italian tutored learners--although having knowledge of some telic verbs of motion--prefer to use the underspecified andare "go" and to build telicity compositionally. The overuse of most frequent and "basic verbs" and the promotion of adjuncts to the rank of real arguments is a challenge for both the Aspect Hypothesis and the parametric view to the acquisition of the tense-aspect system in a second language. (Contains 3 figures, 2 tables, and 1 footnote.)