Residual dipolar coupling constants measured in anisotropic solution contain information on orientations between internuclear vectors and the magnetic field, providing long-range information that may help determine the relative orientations of distinct domains in biomolecules. Here we describe the measurement and use of residual dipolar coupling restraints in the refinement of the structure of the complex of DNA with three zinc fingers of transcription factor IIIA (TFIIIA), measured in a DMPC/DHPC bicelle solution. These dipolar restraints were applied on a variety of orientations of the zinc finger domains (derived from crystallography, previous NMR studies, and systematic modeling) in order to examine the validity and sensitivity of using residual dipolar splittings to study interdomain orientations. The spread in interdomain angles between zinc fingers is reduced from 24 degrees to 9 degrees upon incorporation of dipolar restraints. However, the results also show that the ability to determine relative orientations is strongly dependent on the structural accuracy of the local domain structures.