[en] We have made measurements of the velocity-dependent film thinning in saturated films of He II over the temperature range 1.1 < T < 1.6 K using a new technique. Results from several experimental runs which employ different geometries in general show quantitative agreement with predictions based on the Bernoulli equation made by Kontorovich. The effects of fluid acceleration encountered in these measurements are considered and shown to be small. A recently proposed vapor-replenishment mechanism appears inconsistent with our observations