We describe a new type of presentation that, when consistent, describes a polycyclic group. This presentation is obtained by refining a series of normal subgroups with abelian sections. These presentations can be described effectively in computer-algebra-systems like $ Gap$ or $ Magma$. We study these presentations and, in particular, we obtain consistency criteria for them. The consistency implementation demonstrates that there are situations where the new method is faster than the existing methods for polycyclic groups.