  We present a method to combine next-to-leading order (NLO) matrix elements in
QCD with leading logarithmic parton showers by applying a suitably modified
version of the phase-space-slicing method. The method consists of subsuming the
NLO corrections into a scale-dependent phase-space-slicing parameter, which is
then automatically adjusted to cut out the leading order, virtual, soft and
collinear contributions in the matrix element calculation. In this way a
positive NLO weight is obtained, which can be redistributed by a parton shower
algortihm. As an example, we display the method for single-jet inclusive cross
sections at O(alpha_s) in electroproduction. We numerically compare the
modified version of the phase-space-slicing method with the standard approach
and find very good agreement on the percent level.
