Accepted Wednesday Oct 28, 2009
We show that the gauge-invariant coupling suggested by Pascalutsa removes non-pole terms from the spin-\fth propagator only for a specific choice of free parameter. For the general case the problem can be solved by demanding the invariance of the full Lagrangian under the point-like transformations. It is shown that apart from gauge invariance the original Rarita-Schwinger constraint ensures a correct number of physical degrees of freedom. This is used to constrain couplings in the various applications of the half-integer R-S theories in hadron physics.