Speech sounds tend to co-occur in the speech stream according to specific combinatory patterns predicted from their sonority status [Parker, S. G. (2002). Quantifying the sonority hierarchy. Unpublished doctoral dissertation, University of Massachusetts, Amherst, MA]. This study introduces a measure of spectral complexity, inspired by Shannon entropy, that ranks American English phonemes into a minimal version of the sonority hierarchy: vowels > approximants > nasals > fricatives > affricates > stops. Spectral complexity for every consonant and vowel in the TIMIT database was calculated by first parsing the phonemes into 20-ms segments and computing an FFT. For each short-term FFT, Shannon entropy was computed using the distribution of relative amplitudes (dB) across frequency. Average entropy across the FFTs was used to index spectral complexity for the phonemes, which were then sorted by sonority status. Results of a between-group comparison with spectral complexity as the independent variable and natural class as the dependent variable revealed the existence of six significantly different groups with spectral complexity ranking according to the sonority hierarchy. These findings suggest that Shannon entropy is a reliable acoustic correlate of sonority and may account for the combinatory patterns of co-occurrence of speech sounds in the speech stream.