  We study perturbativeness of chiral nuclear forces in the $^3P_0$ channel. In
previous works, the focus has been on one-pion exchange, and the applicable
window of perturbative pion exchanges has been shown to span from threshold to
the center-of-mass momentum $k \simeq$ 180 MeV. We will examine, instead,
whether cancellation of short and long-range parts can sufficiently soften the
$^3P_0$ chiral force to make it more amenable to perturbation theory. The
result is encouraging, as the combined $^3P_0$ force is shown to be
perturbative up to $k \simeq$ 280 MeV, covering many nuclear-structure
calculations.
