In this article we present a new method for the pruning of unnecessary connections from neural networks created by an evolutionary algorithm (neuro-evolution). Pruning not only decreases the complexity of the network but also improves the numerical stability of the parameter optimisation process. We show results from experiments where connection pruning is incorporated into EANT2, an evolutionary reinforcement learning algorithm for both the topology and parameters of neural networks. By analysing data from the evolutionary optimisation process that determines the networks parameters, candidate connections for removal are identified without the need for extensive additional calculations.