Examination of the significant heights of zero-crossing waves in the Elbe Estuary has yielded two noteworthy results: 1 In the deeper water of the estuary, the value of the quotient relating the significant and the mean wave heights is larger than on the bordering tidal flat. 2. The value of this function is dependent on the height of the waves; on the tidal flat this dependency is considerably more sensitive than in deeper water. With increasing wave height the value of significant wave height divided by mean height becomes smaller The propagation direction of waves moving onto the tidal flat is contingent upon the position of intertidal channels Such channels sharply reduce the possible propagation directions The waves nearly always move up-channel regardless of the wind direction It is possible to derive special wave period and wave height distributions representing the conditions m very shallow water.