  Parton shower Monte Carlo event generators in which the shower evolves from
hard splittings to soft splittings generally use the leading color
approximation, which is the leading term in an expansion in powers of
$1/N_c^2$, where $N_c = 3$ is the number of colors. We introduce a more general
approximation, the LC+ approximation, that includes some of the color
suppressed contributions. There is a cost: each generated event comes with a
weight. There is a benefit: at each splitting the leading soft$\times$collinear
singularity and the leading collinear singularity are treated exactly with
respect to color. In addition, an LC+ shower can start from a state of the
color density matrix in which the bra state color and the ket state color do
not match.
