Establishing, maintaining, and modifying the phase relationships between extensor and flexor muscle groups is essential for central pattern generators in the spinal cord to coordinate the hindlimbs well enough to produce the basic walking rhythm. This paper investigates a simplified computational model for the spinal hindlimb central pattern generator (CPG) that is abstracted from experimental data from the rodent spinal cord. This model produces locomotor-like activity with appropriate phase relationships in which right and left muscle groups alternate while extensor and flexor muscle groups alternate. Convergence to this locomotor pattern is slow, however, and the range of parameter values for which the model produces appropriate output is relatively narrow. We examine these aspects of the model's coordination of left-right activity through investigation of successively more complicated subnetworks, focusing on the role of the synaptic architecture in shaping motoneuron phasing. We find unexpected sensitivity in the phase response properties of individual neurons in response to stimulation and a need for high levels of both inhibition and excitation to achieve the walking rhythm. In the absence of cross-cord excitation, equal levels of ipsilateral and contralateral inhibition result in a strong preference for hopping over walking. Inhibition alone can produce the walking rhythm, but contralateral inhibition must be much stronger than ipsilateral inhibition. Cross-cord excitatory connections significantly enhance convergence to the walking rhythm, which is achieved most rapidly with strong crossed excitation and greater contralateral than ipsilateral inhibition. We discuss the implications of these results for CPG architectures based on unit burst generators.