Experiments on the deepening of a sheared, turbulent, homogeneous layer downwards into a denser, homogeneous layer were conducted in an annular, laboratory tank, similar to, but larger than, that used by Kato and Phillips (1969). It was found that the entrainment rate did not scale on a Richardson Number containing the upper-layer depth as the length scale, but that all two-layer experiments do scale well on the product of a Richardson Number,gΔρW/ρU2, and the ratioU/u*, whereWis a tank dimension and other symbols have their conventional meanings. This result shows that two velocity scales may be necessary to describe turbulent entrainment across a sheared interface.