  We calculate the rate for $e^+e^-$ annihilation into four jets at
next-to-leading order in perturbative QCD, but omitting terms that are
suppressed by one or more powers of $1/\Nc^2$, where $\Nc$ is the number of
colors. The $\cO(\alpha_s^3)$ corrections depend strongly on the jet resolution
parameter $\ycut$ and on the clustering and recombination schemes, and they
substantially improve the agreement between theory and data.
