The rotational structure of the local mode Si-H stretching vibrational bands (n00 A(1)/E), n = 3, 4, and 6, of (H3SiD)-Si-28 have been studied by high-resolution Fourier transform infrared and by photoacoustic laser spectroscopy. The recorded bands have been rotationally analyzed with a Hamiltonian model which makes use of simple arithmetic relations between some of the rovibrational parameters. While the (300 A(1)/E) states were found to be unperturbed, severe perturbations by unknown dark states affect the (400 A(1)/E) and (600 A(1)/E) states for J values exceeding 8. Ab initio calculations have been performed to form the quadratic and the cubic potential energy surfaces which have been used to calculate spectroscopic parameters for the Si-H stretching fundamentals. These results, together with the local mode relations, have been successfully used to model the vibrational dependence of effective rovibrational parameters in the excited local mode states.