  The Wigner Transform (WT) has been extensively used in the formulation of
phase-space models for a variety of wave propagation problems including
high-frequency limits, nonlinear and random waves. It is well known that the WT
features counterintuitive 'interference terms', which often make computation
impractical. In this connection, we propose the use of the smoothed Wigner
Transform (SWT), and derive new, exact equations for it, covering a broad class
of wave propagation problems. Equations for spectrograms are included as a
special case. The 'taming' of the interference terms by the SWT is illustrated,
and an asymptotic model for the Schroedinger equation is constructed and
numerically verified.
