In the Gr¿dyb tidal inlet (Danish Wadden Sea) simple medium to large dunes, which are superimposed on large to very large dunes, increase in size with decreasing grain size under quasi-constant ebb dominated mean flow conditions. The mean height of the superimposed dunes increases from 0.1 m to 0.5 m and the mean dune length from 7 m to 12 m. This happens over a distance of 1.5 km from the inner to the outer part where mean depth (12 m) and the dominant ebb current (1.0 m s-1) remain constant. Over this reach, the grain size changes from 0.6 mm in the inner part to 0.3 mm in the outer part. As the water depth is constant and more than 1 order of magnitude larger than the height of the dunes, these are regarded as being depth-independent. Relationships between dune dimensions and grain size established in previous studies are transformed into more general statements, bed form dimensions being directly related to the form-corrected Shields parameter ($theta$'). In this way, dune dimensions and flow strength/grain size have, for the first time, been directly related to both bed load and free stream velocity in deeper flow systems. The former relationship is based on a recalibrated (form migration) version of the Meyer-Peter and M¿ller bed load formula. Four diagrams describing flow conditions and dune migration rates as a function of grain size and dune length are presented.