Baker's method (based on linear forms in logarithms) and Runge's method (based on the pigeonhole principle) both allow to bound heights of integral points on curves (or even varieties) in certain situations which turn out to be rather different. In this talk, I will explain how one can in some sense mix them and sometimes obtain improved bounds. Surprisingly, this applies in particular to the (geometrically very simple) situation of S-units and I will explain some of the consequences it has for other Diophantine problems.
