  We analyze two-derivative two-nucleon interactions in a combined pionless
effective field theory and large-$N_c$ expansion. At leading order in the
large-$N_c$ expansion, relationships among low-energy constants emerge. We find
these to be consistent with experiment. However, it is critical to correctly
address the subtraction-point dependence of the low-energy constants. These
results provide additional confidence that the dual-expansion procedure is
useful for analyzing low-energy few-body observables.
