A computer model is described which is used to assess the dynamical complexity of a class of networks of spiking neurons with small-world properties. Networks are constructed by forming an initially segregated set of highly intraconnected clusters and then applying a probabilistic rewiring method reminiscent of the Watts-Strogatz procedure to make intercluster connections. Causal density, which counts the number of independent significant interactions among a system’s components, is used to assess dynamical complexity. This measure was chosen because it employs lagged observations, and is therefore more sensitive to temporally smeared evidence of segregation and integration than its alternatives. The results broadly support the hypothesis that small-world topology promotes dynamical complexity, but reveal a narrow parameter range within which this occurs for the network topology under investigation, and suggest an inverse correlation with phase synchrony inside this range.