This study investigates the effect of alternating growth and pruning phases on the evolution of neural architectures using the Evolutionary eXploration of Augmenting Memory Models (EXAMM). Our objective was to determine if this structured evolutionary process could guide the search towards more compact models without sacrificing predictive performance. We compared EXAMM-evolved architectures having traditional and five modern memory cells (simple, UGRNN, MGU, GRU, Delta-RNN, and LSTM) on two distinct time-series datasets: aviation flight recorder data and wind turbine sensor data. The alternating phases were controlled by enabling growth-promoting or growth-reducing mutation operations based on trigger frequencies of 50, 100, or 200 generated genomes, resulting in a 3 \(\times \) 3 set of nine unique grow-shrink configurations. Results show that while there was no statistical difference in terms of model performance to a baseline without phases, the experiments with higher pruning to growth ratios had statistically significant decreases in model size, making this a simple but effective method for controlling network complexity.