Duct coupling, in which part of the energy of a downcoming whistler-mode wave becomes trapped in a different duct after upward reflection in the ionosphere, manifests itself in the phenomenon of the mixed-path whistler. Using VLF data from direction-finding receivers at Halley and Palmer stations, Antarctica, we analyse a case near dawn in which the path structure was particularly simple. One-hop and three-hop whistlers observed at both stations implied the existence of two ducts inside the plasmasphere (at L ~ 3) and of wave coupling between them. The most intense of the three-hop echoes was a mixed-path rather than a single-path component; this is explained in terms of bi-directional coupling between the ducts in both northern and southern conjugate ionospheres. The locations of the ionospheric exit points for signals leaving the ducts were found from whistler arrival bearings measured at the two stations (the first results of crossed bearings from the IMS Antarctic VLF observing programme); these points were about 300 km apart. An echo trace seen only on the Halley record implied coupling to a third path outside the plasmapause (at Lpp ≅ 3.3). We discuss the significance of such path coupling in relation to the spreading of ducted and unducted wave energy in the magnetosphere, and to the triggering of chorus.