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The efficiency of two-photon-pumped frequency converters as a function of the pump laser detuning and linewidth, and of the linewidth of the selected nonallowed atomic transition is studied. We show that pressure broadening of the atomic transition is a key parameter in the design of these converters. A technique is developed to measure this linewidth as a function of either self- or foreign-gas broadening using a broad-band pump laser. Measurements of the linewidth of the transition of Na, and its device implications, are presented.