  One can use more than one scale variable to specify the family of surfaces in
the space of parton splitting parameters that define the evolution of a parton
shower. Considering $e^+e^-$ annihilation, we use two variables, with shower
evolution following a special path in this two dimensional space. In addition,
we treat in a special way the part of the splitting function that has a soft
emission singularity but no collinear singularity. This leads to certain
advantages compared to the usual shower formulation with only one scale
variable.
