In order to perform a nonlinear dimensional analysis of the sleep electroencephalogram (EEG), we applied an algorithm proposed by Grassberger and Procaccia to calculate the correlation dimension D2 of different sleep stages under Lorazepam medication versus placebo. This correlation dimension characterizes the dynamics of the sleep EEG and it estimates the degrees of freedom of the signal under study. We demonstrate that slow-wave sleep depicts a much smaller dimensionality than light or rapid eye movement (REM) sleep, and that Lorazepam does not alter the EEG's dimensionality except in stage II and REM.