Dosage sensitivity is an important evolutionary force which impacts on gene dispensability and duplicability. The newly available data on human copy-number variation (CNV) allow an analysis of the most recent and ongoing evolution. Provided that heterozygous gene deletions and duplications actually change gene dosage, we expect to observe negative selection against CNVs encompassing dosage sensitive genes. In this study, we make use of several sources of population genetic data to identify selection on structural variations of dosage sensitive genes. We show that CNVs can directly affect expression levels of contained genes. We find that genes encoding members of protein complexes exhibit limited expression variation and overlap significantly with a manually derived set of dosage sensitive genes. We show that complexes and other dosage sensitive genes are underrepresented in CNV regions, with a particular bias against frequent variations and duplications. These results suggest that dosage sensitivity is a significant force of negative selection on regions of copy-number variation.