We use a range of morpho-syntactic features inspired by research in register studies (e.g. Biber, 1995; Neumann, 2013) and translation studies (e.g. Ilisei et al., 2010; Zanettin, 2013; Kunilovskaya and Kutuzov, 2018) to reveal the association between translationese and human translation quality. Translationese is understood as any statistical deviations of translations from non-translations (Baker, 1993) and is assumed to affect the fluency of translations, rendering them foreign-sounding and clumsy of wording and structure. This connection is often posited or implied in the studies of translationese or translational varieties (De Sutter et al., 2017), but is rarely directly tested. Our 45 features include frequencies of selected morphological forms and categories, some types of syntactic structures and relations, as well as several overall text measures extracted from Universal Dependencies annotation. The research corpora include English-to-Russian professional and student translations of informational or argumentative newspaper texts and a comparable corpus of non-translated Russian. Our results indicate lack of direct association between translationese and quality in our data: while our features distinguish translations and non-translations with the near perfect accuracy, the performance of the same algorithm on the quality classes barely exceeds the chance level.