We present an experimental analysis of the influence of the local irregularity of the fitness function on the behavior of a simple version of an evolutionary algorithm (EA). Previous theoretical as well as experimental work on this subject suggest that the performance of EA strongly depends on the irregularity of the fitness function. Several irregularity measures have been derived, in order to numerically characterize this type of difficulty source for EA. These characterizations are mainly based on Hölder exponents. Previous studies used a global characterization of fitness regularity (namely the global Hölder exponent), with experimental validations being conducted on test functions with uniform irregularity. The present work refines the analysis by investigating the behavior of an EA on functions displaying variable local regularity. Our experiments confirm and quantify the intuition that performance decreases as irregularity increases. In addition, they suggest a way to modify the genetic topology to accommodate for variable regularity: More precisely, it appears that the mutation parameter, which controls the size of the neighbourhood of a point, should increase when regularity decreases. These results open the way to a theoretical analysis based on local Hölder exponents, and poses several questions with respect to on-line measurements and usage of regularity for fitness functions.