We present a new set of 96 Swedish multi-word expressions annotated with degree of (non-)compositionality. In contrast to most previous compositionality datasets we also consider syntactically complex constructions and publish a formal specification of each expression. This allows evaluation of computational models beyond word bigrams, which have so far been the norm. Finally, we use the annotations to evaluate a system for automatic compositionality estimation based on distributional semantics. Our analysis of the disagreements between human annotators and the distributional model reveal interesting questions related to the perception of compositionality, and should be informative to future work in the area.