In this article we focus on one grammaticalization path to perfective markers, that of the so-called "bounder perfectives" (Bybee and Dahl 1989). Systems with this kind of perfective markers - often called "Slavic-style aspect" -- are particular elaborated in the Slavic languages. To examine why this is the case, we study the long-disputed question of the semantic relationship between the inflectional aspectual system inherited from PIE and the emerging affixation-based verb pair system in expressing aspect in Old Church Slavonic (OCS), using parallel Greek and OCS data from the PROIEL corpus. Previous researchers have made extremely conflicting claims about this relationship, some seeing the inflectional system as the main exponent of aspect, others seeing the affixation system as the main exponent of aspect. Our statistical study of the data shows rather that the OCS system attests an interesting language stage where there are two partially overlapping exponents of aspect. By firmly establishing the facts of the synchronic OCS system, we can look both backwards and forwards. We argue that Slavic "bounder perfectives" owe their advanced development to their coexistence with the old inflectional aspect system. We also argue that the well-known interactions between the two aspectual systems in Bulgarian, which still retains both, are probably a later development.