We present a Slovene combined machine-human translated SuperGLUE benchmark. We describe the translation process and problems arising due to differences in morphology and grammar. We evaluate the translated datasets in several modes: monolingual, cross-lingual, and multilingual, taking into account differences between machine and human translated training sets. The results show that the monolingual Slovene SloBERTa model is superior to massively multilingual and trilingual BERT models, but these also show a good cross-lingual performance on certain tasks. The performance of Slovene models still lags behind the best English models.