Memory-augmented neural networks (MANNs) can perform algorithmic tasks such as sorting. However, they often fail to generalise to input sequence lengths not encountered during training. We introduce two approaches that constrain the state space of the MANN's controller network: state compression and state regularisation. We empirically demonstrated that both approaches can improve generalisation to input sequences of out-of-distribution lengths for a specific type of MANN: the differentiable neural computer (DNC). The constrained DNC could process input sequences that were up to 2.3 times longer than those processed by an unconstrained baseline controller network. Notably, the applied constraints enabled the extension of the DNC's memory matrix without the need for retraining and thus allowed the processing of input sequences that were 10.4 times longer. However, the improvements were not consistent across all tested algorithmic tasks. Interestingly, solutions that performed better often had a highly structured state space, characterised by state trajectories exhibiting increased curvature and loop-like patterns. Our experimental work demonstrates that state-space constraints can enable the training of a DNC using shorter input sequences, thereby saving computational resources and facilitating training when acquiring long sequences is costly.