Rubisco assumes the double role of accumulating biomass by fixing carbon dioxide to ribulose-1,5-bisphosphate and binding of molecular oxygen to the same substrate. The specificity factor of this mutually competitive activity, defined as the ratio of carboxylation to oxygenation efficiency, varies considerably for reasons which remain obscure. The explanation and the enhancement of specificity are of high theoretical and practical interest. Despite a wealth of structures and experimental findings, the systematic analysis of available data is still at its beginning. Here, we (a) present an analysis of sequences of the large subunit which reliably finds specificity-enhancing mutations and ranks them according to the probability of success. For mutations near the C-terminus, we (b) show by simulations that the positive influence they have on specificity can be explained by the time-window hypothesis.