Following up on an earlier paper demonstrating statistically significant relationships between measures of recurring political-economic crises (hinterland incursions, trade collapses, economic contractions, and regime transitions) and a measure of climate deterioration (the interaction of falling Tigris-Euphrates river levels and years of warming/drying), the inter-relationships among these variables are examined more closely for the 3400–1000 BCE period. Theoretically focused on a test of Tainter’s diminishing marginal return theory of societal collapse, additional indicators are introduced encompassing population (urban population size, urban population growth rate) as a proxy for diminishing marginal returns, two measures of centralization/ fragmentation (including imperial size), and the indicators used for the climate interaction term in the earlier paper. The multivariate logit outcome for interactions among and between the 11 variables reinforces the earlier findings linking climate deterioration to political-economic crises, extends the climate deterioration linkage to fragmentation and population decline, and finds relatively strong support for the Tainter derived expectation that diminishing marginal returns and fragmentation are closely linked but that both are less closely linked to recurring political-economic crises than might otherwise have been anticipated.