Recent optimism about sustainability has centred on the opportunities for improvements in environment-efficiency through the international diffusion of environmentally-beneficial innovations. This paper investigates two claims about the conditions under which countries are most likely to realise these gains. First, “dirtier” economies should improve their environment-efficiency faster, as they adopt environmentally sound technologies and policies similar to those in “cleaner” countries, resulting in catch-up and convergence over time. Second, transnational linkages accelerate the international spread of environmentally-beneficial innovations, and therefore improvements in environment-efficiency. To test these claims, we use econometric techniques to examine the dynamics and determinants of two pollutants, CO2 and SO2, using a panel comprising up to 114 countries over the period 1980-2000. Our empirical findings broadly support both claims. Applying tests of unconditional convergence, we find robust evidence for convergence in levels of CO2 and SO2-efficiency, indicating catch-up by less pollution-efficient economies over time. Similarly, confirming claims about transnational linkages, we find that imports from more pollution-efficient countries and telecommunications connectivity are associated with faster improvements in domestic CO2 and SO2-efficiency. Results also suggest that inward FDI stock is positively associated with CO2-efficiency. Yet we find that exports to countries with high levels of pollution-efficiency have no discernable effect on domestic pollution-efficiency.