From modelling studies it has been known for over ten years that purely inhibitory networks can produce synchronous output given appropriate balances of intrinsic and synaptic parameters. Several experimental studies indicate that synchronous activity produced by inhibitory networks is critical to the production of population rhythms associated with various behavioural states. Heterogeneity of inputs to inhibitory networks strongly affect their ability to synchronize. In this paper, we explore how the amount of input heterogeneity to two-cell inhibitory networks affects their dynamics. Using numerical simulations and bifurcation analyses, we find that the ability of inhibitory networks to synchronize in the face of heterogeneity depends non-monotonically on each of the synaptic time constant, synaptic conductance and external drive parameters. Because of this, an optimal set of parameters for a given cellular model with various biophysical characteristics can be determined. We suggest that this could be a helpful approach to use in determining the importance of different, underlying biophysical details. We further find that two-cell coherence properties are maintained in larger ten-cell networks. As such, we think that a strategy of "embedding" small network dynamics in larger networks is a useful way to understand the contribution of biophysically-derived parameters to population dynamics in large networks.