  Nonrelativistic bound states have two low energy scales, a soft scale mu_S of
order mv and an ultrasoft scale mu_U of order mv^2. In two-stage running, the
soft and ultrasoft scales are lowered from m to mv, and then the ultrasoft
scale is lowered from mv to mv^2. In one-stage running, the two scales are
lowered in a correlated way using a subtraction velocity. We compare these two
methods of summing logarithms and show that only the correlated running in
velocity space of the one-stage method correctly reproduces the logarithms in
non-relativistic bound states in QED. The argument for one-stage running is
general, and should apply to any system with correlated scales.
