The success of an ENSO-based statistical rainfall prediction scheme and the influence of ENSO on Australia are shown to vary in association with a coherent, inter-decadal oscillation in surface temperature over the Pacific Ocean. When this Inter-decadal Pacific Oscillation (IPO) raises temperatures in the tropical Pacific Ocean, there is no robust relationship between year-to-year Australian climate variations and ENSO. When the IPO lowers temperature in the same region, on the other hand, year-to-year ENSO variability is closely associated with year-to-year variability in rainfall, surface temperature, river flow and the domestic wheat crop yield. The contrast in ENSO's influence between the two phases of the IPO is quite remarkable. This highlights exciting new avenues for obtaining improved climate predictions.