We argue that the interpretation of transitive aspectual-verb sentences like “Sue finishes the book” results from an evaluation of the degree of asymmetry in control power between the participants in the sentence. Control asymmetry is proposed as one conceptual constraint on sentence meaning precisification. An evaluation of ‘high control asymmetry’ for the relation between “Sue” and “book” yields an agentive/actor-undergoer interpretation (Sue is doing something involving the book). An evaluation of ‘low control asymmetry’ yields a constitutive/part–whole interpretation (Sue’s story is the last one in the book). Which reading emerges depends on the comprehender’s control-asymmetry evaluation based on contextual cues or, in the absence of explicit context, based on conventionalized control asymmetry expectations given the participants’ denotations. Results show that semantically under-specified aspectual-verb sentences such as “Sue finishes/begins/continues the book” (i) receive multiple readings in a control-asymmetry neutral context, (ii) are judged as less acceptable than their control asymmetry-biased counterparts, and (iii) clearly evidence the constitutive reading as part of their core reading. These findings are consistent with a real-time linguistic meaning composition system that systematically draws from context guided by lexically driven semantic demands and that presents the structure of these demands as a cognitively viable metric of complexity.