  We propose a new method to implement the running coupling constant in the
JIMWLK equation, imposing the scale dependence on the correlation function of
the random noise in the Langevin formulation. We interpret this scale choice as
the transverse momentum of the emitted gluon in one step of the evolution and
show that it is related to the "Balitsky" prescription for the BK equation.
This slows down the evolution speed of a practical solution of the JIMWLK
equation, bringing it closer to the x-dependence inferred from fits to HERA
data. We further study our proposal by a numerical comparison of the BK and
JIMWLK equations.
