We use Universal Dependencies treebanks to test whether a well-known typological trade-off between word order freedom and richness of morphological marking of core arguments holds within individual languages. Using Russian and German treebank data, we show that the following phenomenon (sometimes dubbed word order freezing) does occur: those sentences where core arguments cannot be distinguished by morphological means (due to case syncretism or other kinds of ambiguity) have more rigid order of subject, verb and object than those where unambiguous morphological marking is present. In ambiguous clauses, word order is more often equal to the one which is default or dominant (most frequent) in the language. While Russian and German differ with respect to how exactly they mark core arguments, the effect of morphological ambiguity is significant in both languages. It is, however, small, suggesting that languages do adapt to the evolutionary pressure on communicative efficiency and avoidance of redundancy, but that the pressure is weak in this particular respect.