I survey cases of contact-induced influence of Slavic and Baltic systems of prefixal perfectivization on Yiddish, Romani, Livonian and Istroromanian. I show that, although both matter and pattern borrowing of entire systems of Slavic or Baltic verbal prefixes is attested, grammatical aspectual categories similar to those of the donor languages do not arise in the contact languages, or develop in a way distinct from the donor languages (as in Istroromanian). This indicates that abstract grammatical oppositions such as "Slavic-style" aspect are immune to direct transfer in language contact.