  We investigate, theoretically and experimentally, absorption on an
excited-state atomic transition in a thermal vapor where the lower state is
coherently pumped. We find that the transition linewidth can be sub-natural,
i.e. less than the combined linewidth of the lower and upper state. For the
specific case of the 6P_{3/2} -> 7S_{1/2} transition in room temperature cesium
vapor, we measure a minimum linewidth of 6.6 MHz compared with the natural
width of 8.5 MHz. Using perturbation techniques, an expression for the complex
susceptibility is obtained which provides excellent agreement with the measured
spectra.
