The spread of electroencephalography (EEG) in countless applications has fostered the development of new techniques for extracting synthetic and informative features from EEG signals. However, the definition of an effective feature set depends on the specific problem to be addressed and is currently an active field of research. In this work, we investigated the application of features based on fractal dimension to a problem of sleep identification from EEG data. We demonstrated that features based on fractal dimension, including two novel indices defined in this work, add valuable information to standard EEG features and significantly improve sleep identification performance.