Neurocontroller minimization is beneficial for constructing small parsimonious networks that permit a better understanding of their workings. This paper presents a novel, Evolutionary Network Minimization (ENM) algorithm which is applied to fully recurrent neurocontrollers. ENM is a simple, standard genetic algorithm with an additional step in which small weights are irreversibly eliminated. ENM has a unique combination of features which distinguish it from previous evolutionary minimization algorithms: 1. An explicit penalty term is not added to the fitness function. 2. Minimization begins after functional neurocontrollers have been successfully evolved. 3. Successful minimization relies solely on the workings of a drift that removes unimportant weights and, importantly, on continuing adaptive modifications of the magnitudes of the remaining weights. Our results testify that ENM is successful in extensively minimizing recurrent evolved neurocontrollers while keeping their fitness intact and maintaining their principal functional characteristics.