Rhythmicity is a characteristic of neural networks responsible for locomotion. In many organisms, activation of N-methyl-D: -aspartate (NMDA) receptors leads to generation of rhythmic locomotor patterns. In addition, single neurons can display intrinsic, NMDA-dependent membrane potential oscillations when pharmacologically isolated from each other by tetrodotoxin (TTX) application. Such NMDA-TTX oscillations have been characterized, for instance, in lamprey locomotor network neurons. Conceptual and computational models have been put forward to explain the appearance and characteristics of these oscillations. Here, we seek to refine the understanding of NMDA-TTX oscillations by combining new experimental evidence with computational modelling. We find that, in contrast to previous computational predictions, the oscillation frequency tends to increase when the NMDA concentration is increased. We develop a new, minimal computational model which can incorporate this new information. This model is further constrained by another new piece of experimental evidence: that regular-looking NMDA-TTX oscillations can be obtained even after voltage-dependent potassium and high-voltage-activated calcium channels have been pharmacologically blocked. Our model conforms to several experimentally derived criteria that we have set up and is robust to parameter changes, as evaluated through sensitivity analysis. We use the model to re-analyze an old NMDA-TTX oscillation model, and suggest an explanation of why it failed to reproduce the new experimental data that we present here.