  We solve the Balitsky-Kovchegov evolution equation at next-to-leading order
accuracy including a resummation of large single and double transverse momentum
logarithms to all orders. We numerically determine an optimal value for the
constant under the large transverse momentum logarithm that enables including a
maximal amount of the full NLO result in the resummation. When this value is
used the contribution from the $\alpha_s^2$ terms without large logarithms is
found to be small at large saturation scales and at small dipoles. Close to
initial conditions relevant for phenomenological applications these fixed order
corrections are shown to be numerically important.
