Features of sleep were shown to reflect aging, typical sex differences and cognitive abilities of humans. However, these measures are characterized by redundancy and arbitrariness. Our present approach relies on the assumptions that the spontaneous human brain activity as reflected by the scalp-derived electroencephalogram (EEG) during non-rapid eye movement (NREM) sleep is characterized by arrhythmic, scale-free properties and is based on the power law scaling of the Fourier spectra with the additional consideration of the rhythmic, oscillatory waves at specific frequencies, including sleep spindles. Measures derived are the spectral intercept and slope, as well as the maximal spectral peak amplitude and frequency in the sleep spindle range, effectively reducing 191 spectral measures to 4, which were efficient in characterizing known age-effects, sex-differences and cognitive correlates of sleep EEG. Future clinical and basic studies are supposed to be significantly empowered by the efficient data reduction provided by our approach.