Quenched directional solidification of specially oriented bi-crystals of the Ni-base superalloy CMSX4, was carried out in an attempt to understand the role of the dendritic morphology in the process of competitive grain growth. For the range of misorientations considered (primary <001> misoriented by up to 7degrees from the uniaxial thermal gradient), there was no evidence of overgrowth of the primary misoriented dendrite by the secondary arms on the leading aligned primary. In fact, it was observed that for this range of misorientations, the tip of the retarded primary suppresses the growth of secondaries on its leading neighbour. This subsequently simply restricts the growth of the mis-aligned crystal to its original boundary, rather than reducing its size and is suggested as a possible reason for the range of stable axial orientations encountered during directional solidification of CMSX4.