Dimensionally similar discharges are investigated in ASDEX Upgrade, JET and ALCATOR C-Mod to study critical parameters for the H-mode transition and the boundary of the "Enhanced D-Alpha" (EDA) H-mode regime. Comparison of JET and ASDEX Upgrade confirms that the H-mode transition can be obtained at same values of r*, n*, b at the edge and rules out the absolute temperature T as a similarity parameter. Attempts to reproduce the EDA regime of ALCATOR C-Mod in ASDEX Upgrade have not been successful. The matching pedestal collisionality is found inaccessible due to H L back-transition. Possible reasons for the mismatch of the H-mode boundary are discussed.