Neural network pruning methods on the level of individual network parameters (e.g. connection weights) can improve generalization, as is shown in this empirical study. However, an open problem in the pruning methods known today (e.g. OBD, OBS, autoprune, epsiprune) is the selection of the number of parameters to be removed in each pruning step (pruning strength). This work presents a pruning method Iprune that automatically adapts the pruning strength to the evolution of weights and loss of generalization during training. The method requires no algorithm parameter adjustment by the user. Results of statistical significance tests comparing autoprune, Iprune, and static networks with early stopping are given, based on extensive experimentation with 14 different problems. The results indicate that training with pruning is often significantly better and rarely significantly worse than training with early stopping without pruning. Furthermore, Iprune is often superior to autoprune (which is superior to OBD) on diagnosis tasks unless severe pruning early in the training process is required.