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Tropical modes of variability, such as El Niño–Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD), exert a strong influence on the interannual variability of Australian precipitation. Nevertheless, commonly used indices of ENSO and IOD variability display significant co-variability that prevents a robust quantification of the independent contribution of each mode to precipitation anomalies. This co-variability issue is often addressed by statistically removing ENSO or IOD variability from the precipitation field before calculating teleconnection patterns. However, by performing a suite of coupled and uncoupled modelling experiments in which either ENSO or IOD variability is physically removed, we show that ENSO-only-driven precipitation patterns computed by statistically removing the IOD influence significantly underestimate the impact of ENSO on Australian precipitation variability. Inspired by this, we propose a conceptual model that allows one to effectively separate the contribution of each mode to Australian precipitation variability.