A steady-state solution describing π-pulse propagation in a homogeneously broadened laser amplifier embedded in a dispersive lossy host is found. For a given model of dispersion, the solution satisfies exactly the second-order wave equation together with the equations of motion for the density matrix of the two-level resonant system. The salient feature of the solution is that a small amount of dispersion in the host group velocity causes a large monotonic frequency sweep during the pulse. The effects of this chirp on the pulse properties are described in detail, and the relation of the theory to experiments is discussed. Copyright © 1969 by The Institute of Electrical and Electronics Engineers, Inc.