The classical Rellich inequalities imply that the ; ; ; ; L; 2; ; L^2; ; ; -norms of the normal and tangential derivatives of a harmonic function are equivalent. In this note, we prove several refined inequalities, which make sense even if the domain is not Lipschitz. For two-dimensional domains, we obtain a sharp ; ; ; ; L; p; ; L^p; ; ; -estimate for ; ; ; ; 1; >; p; ≤; 2; ; 1>pleq 2; ; ; by using a Riemann mapping and interpolation argument.