Overdeepenings are a hallmark glacial landform of broad geomorphologlogical and glaciological interest. Their formation mechanism has not yet been fully uncovered, but subglacial drainage is likely a key factor. One prominent hypothesis states that the depth of an overdeepening stabilizes at the supercooling threshold. This threshold is reached when the adverse bed slope terminating an overdeepening is sufficiently large to shut down the efficient, channelized drainage system. Classic theory puts this threshold at a ratio of bed to surface slope of − 1.6. Here I extend that theory by taking into account that downstream water pressure can be below overburden pressure. The new formula agrees well with results from one- and two-dimensional subglacial drainage models. Applying it to observations of 147 overdeepenings from alpine glaciers and ice sheets shows that the depth of overdeepenings rarely exceeds the new supercooling threshold. Thus, this work supports the stabilizing hypothesis.