  Runge's method is a tool to figure out integral points on curves effectively
in terms of height. This method has been generalised to varieties of any
dimension, unfortunately its conditions of application are often too
restrictive. In this paper, we provide a further generalisation intended to be
more flexible while still effective, and exemplify its applicability by giving
finiteness results for integral points on some Siegel modular varieties. As a
special case, we obtain a totally explicit finiteness result for integral
points on the Siegel modular variety $A_2(2)$.
