  Parton shower Monte Carlo event generators in which the shower evolves from
hard splittings to soft splittings generally use the leading color (LC)
approximation, which is the leading term in an expansion in powers of
$1/N_\Lc^2$, where $N_\Lc = 3$ is the number of colors. In the parton shower
event generator \textsc{Deductor}, we have introduced a more general
approximation, the LC+ approximation, that includes some of the color
suppressed contributions. In this paper, we explore the differences in results
between the LC approximation and the LC+ approximation. Numerical comparisons
suggest that, for simple observables, the LC approximation is quite accurate.
We also find evidence that for gap-between-jets cross sections neither the LC
approximation nor the LC+ approximation is adequate.
