An optimization procedure for determining the force constant parameters of a simple 'eleven-parameter' rigid-ion model (RIM) has been developed that yields good predictive power for the eigendisplacements (EDs). The disregard that the RIM has fallen into in the last few decades is undeserved, and here the authors show that given an appropriately optimized set of parameters the RIM can predict good results. The optimization procedure is presented and applied here to SiC and GaAs. For SiC the optimized parameters not only give calculated phonon frequencies which agree with the measurements to better than 6% but also predict the EDs which agree with the ab initio (LDF) method to better than 1%. In the case of GaAs the RIM, using the optimized parameters, predicts the observed EDs to well within the quoted experimental uncertainties. Where the measurements do not exist, the predicted EDs in GaAs agree with those calculated by the LDF method to better than 1%. As is the case of the LDF method calculations on GaAs, the present RIM calculations for the transverse acoustic (TA) frequencies show large variations from the measured values towards the zone boundaries. This implies that short-range forces from further neighbours need to be taken into account if the calculated frequencies are also to agree with the measurements. The RIM calculations presented here of EDs in SiC and GaAs using the set of force constant parameters optimized for that purpose, suggest that these calculations are essentially model independent.