This paper explores the use of a Monte Carlo adaptation of runs analysis to analyze turbidite sequences for the presence of asymmetric bed-thickness cycles. Waldron's test can be used to identify sequences that are dominated by either upward-thickening or upward-thinning cycles, but not both. Our adaptation of runs analysis provides a robust technique that can indicate the presence of local thickness trends that are different from those expected in random sequences, and can be used to evaluate the relative importance of upward-thickening and upward-thinning cycles. As a case study, 236 m of the Upper Cretaceous Sites Formation in the Great Valley Group were measured and described in detail along Cache Creek in northern California. This section had been previously interpreted as a succession of prograding submarine-fan-lobe deposits marked by asymmetric upward-thickening cycles. Application of Waldron's test indicates that the section is not dominated by upward-thickening cycles, as previously suggested. Monte Carlo runs analysis demonstrates that small-scale upward-thinning cycles are as common as upward-thickening cycles. The simple progradation of submarine fan lobes does not adequately explain the thickness patterns seen in the section. Application of Monte Carlo runs analysis to other turbidite sections would be useful for quantitative identification and comparison of turbidite bed-thickness cycles, which should lead to development of better turbidite facies models.