  We describe a new type of polycyclic presentations, that we will call refined
solvable presentations, for polycyclic groups. These presentations are obtained
by refining a series of normal subgroups with abelian sections. These
presentations can be described effectively by presentation maps which yield the
basis data structure to define a polycyclic group in computer-algebra-systems
like {\scshape Gap} or {\scshape Magma}. We study refined solvable
presentations and, in particular, we obtain consistency criteria for them. This
consistency implementation demonstrates that it is often faster than the
existing methods for polycyclic groups.
