The authors examine the evolution of inhomogeneities (fragments) of supernova ejecta in compact supernova remnants by means of hydrodynamical modelling and simplified analytical calculations. Under the influence of intense post-shock cooling the fragments become strongly compressed as they traverse the hot shocked region between the reverse and outer shocks of the remnants. The authors find that the most likely outcome of the interaction of fragments with the reverse shock and the hot shocked region is their disruption, resulting in the generation of secondary fragments. Secondary fragments arriving at the thin and dense outer shell of the remnant give rise to brief X-ray flashes. Under suitable conditions the primary fragments may traverse the hot shocked region without being completely destroyed, eventually reaching the outer shell as dense, elongated structures. Collisions of such fragments with the shell are likely to give rise to powerful X-ray flares.