We propose that the distribution of layer thicknesses of turbidite deposits that show minimal erosional truncation and amalgamation should obey the power law N(h) congruent to h (super -B) , where N(h) is the number of layers of thickness greater than h and B congruent to 1. We support this proposal with two sets of observations, one from formation-microscanner images obtained in offshore wells that penetrate Tertiary fore-arc turbidites (Hiscott et al. 1992) and the other from our own field measurements of turbidites in the Neoproterozoic Kingston Peak Formation, deposited in a glacially influenced rift basin. Both sets of observations show roughly the same power-law distribution above a small-h cutoff. Motivated by the possible generality of these results, and given strong geological and sedimentological contrasts between the two data sets, we consider the available theoretical and experimental evidence that could support or deny these observations. We tentatively conclude that the power law is generic in data sets characterized by minimal erosional truncation and amalgamation but emphasize that further study is required for a definitive statement. Proceeding from the assumption that the scaling law is valid for arbitrarily thin layers, we derive an upper bound for B. We then detail simple and plausible assumptions that provide a theoretical estimate of B. We discuss possible ramifications of this analysis for the interpretation of further data.