  We present a systematic and quite elementary method for constructing discrete
Painlev\'e equations in the degeneration cascade for E$_8^{(1)}$. Starting from
the invariant for the autonomous limit of the E$_8^{(1)}$ equation one wishes
to study, the method relies on choosing simple homographies that will cast this
invariant into certain judiciously chosen canonical forms. These new invariants
lead to mappings the deautonomisations of which allow us to build up the entire
degeneration cascade of the original mapping. We explain the method on three
examples, two symmetric mappings and an asymmetric one, and we discuss the link
between our results and the known geometric structure of these mappings.
