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For small primary feeds the radiation field is determined numerically, using an integral-equation formulation for the surface currents and its solution by a moment method. The computed fields are used to determine the feed-phase centres, as defined to minimise the phase variation of the field over a selected angular region, or to maximise the reflector gain factor. Both circular and coaxial waveguides, with and without a corrugated flange, are considered. For the corrugation geometry, the commonly used rectangular shape and a trapezoidally-profiled one are studied. It is shown that the location and the uniqueness of the feed-phase centre depend on waveguide dimensions, the corrugation number, their location and shape. For an optimum phase-centre location, the resulting phase errors, over a selected angular region, are also determined.