  We present a method to obtain rapid mass loss rates in binary systems,
specifically at the onset of MT episodes. The method unifies atmospheric
(underflow) and $L_1$ stream (overflow) mass rates in a single continuous
procedure. The method uses averaged 3D properties of the binaries, such as
effective binary potential and effective binary acceleration, to both evolve
the donor and obtain properties of the matter at the $L_1$ plane. In the case
of underflow, we obtain atmospheric stratification. Our method can be used for
binaries with an extensive range of mass ratios, $0.01 \le q \le 100$, and can
also be applied to hot donors. The considered examples show that the MT rates
obtained with this revised formalism always differ from the optically thin and
optically thick MT rates widely used during the computations of binary
evolution.
