We experimentally report a surprising linewidth narrowing of the direct exitonic 1 s heavy-hole transition in a type-II quantum well system. This narrowing, which builds up on a pico- to nanosecond timescale, causes a transient enhanced absorption at the spectral peak position of the excitonic resonance. We discuss how this effect depends on experimental parameters such as excitation density, temperature, and barrier width. We cannot attribute this effect to known physical mechanisms.