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Some aspects of the propagation of scalar waves in bounded, randomly fluctuating media are considered. Specifically emphasized are the interface effects on the coherent wave motion in the limit of small-scale fluctuations. It is shown that the procedure whereby a bounded, fluctuating region is replaced by an effectively homogeneous medium whose properties follow from the analysis of the appropriate unbounded domain may not be applicable, and an effectively inhomogeneous profile is generally required. In the case of fluctuations in a one-dimensional medium bounded by a planar interface (for which explicit solutions are found), we conclude that the interface perturbs the coherent wave motion to a significant extent over a large distance from it. The three-dimensional model reveals several deviations from the corresponding one-dimensional case; the most significant stems from the observation that the interface effects are now confined to a well-defined ‘transition’ layer of the order of a wavelength in thickness.