The relationships between the entropy production per cycle and the thermal efficiency are investigated for a class of irreversible cyclic processes. Examples are given that pinpoint specific sources of irreversibility and their thermodynamic consequences. It is found that an increase (decrease) in an irreversible cycle’s thermal efficiency does not necessarily lead to a decrease (increase) in its entropy production even if the work done per cycle is held constant. Only for the case of a reversible Carnot cycle is it guaranteed that a change (negative for this case) in the efficiency is met by an entropy production change of opposite algebraic sign. Sufficiency conditions are found for which the entropy production and the efficiency η are inversely related for more general cyclic processes. For a given set of heat reservoirs and specified values of the work output W, the absolute minimum and maximum entropy productions are determined and are shown to be monotonically decreasing functions of η for fixed W. It is shown also that, for an irreversible cycle with maximum and minimum temperatures T+and T−, respectively, η? (1−T−/T+)(1+T−ΔS/W)−1, where ΔS is the entropy production per cycle. The equality holds only for a cycle employing two reservoirs. The potential relevance of these results to environmental and technological problems is mentioned.