The widespread occurrence of discontinuous gullies in the oil-shale region of northwestern Colorado is of particular concern because of the resulting progressive destruction of the valley floors. Furthermore, the integration of a semi-arid drainage network can cause a rapid increase in the sediment yield of the basin, with subsequent harmful effects downstream. Field work in the Piceance Creek and Yellow Creek drainage basins indicates that these discontinuous gullies developed on oversteepened segments of the valley floors. Although the critical slope of entrenchment is probably related to magnitude of run-off, discharge measurements are not available; therefore, drainage-basin area was selected as the most representative measure of discharge. An inverse relation between drainage-basin area and critical slope of entrenchment applies, and the lower limit of scatter of the data establishes a critical slope-area relation, which can be used to identify potentially unstable valley floors. This relation can help the land manager determine areas of instability where preventive measures can most economically and successfully be undertaken. It is stressed that this particular quantitative relation is applicable only to the Piceance Creek and Yellow Creek drainage basins. In more heterogeneous basins, other variables will need to be included in the analysis; however, the general theory of valley stability will remain applicable.