In austral summer, El Niño-Southern Oscillation (ENSO) covaries with the Indian Ocean Basin Mode (IOBM) and with the southern annular mode (SAM). The present study addresses how the IOBM and the SAM modulate the impact of ENSO on Australia. The authors show that the modulating effect of the SAM is limited; in particular, the SAM does not modify the ENSO teleconnection pattern. However, the IOBM extends ENSO-induced convection anomalies westward over northern Australia and over the eastern Indian Ocean, whereby extending the ENSO tropical teleconnection to the northwest of Australia. The IOBM also generates an equivalent-barotropic Rossby wave train through convection anomalies over northern Australia. The wave train shares an anomaly center over the Tasman Sea latitudes with the Pacific-South American (PSA) pattern, shifting the anomaly center of the PSA pattern to within a closer proximity to Australia. There is a strong asymmetry in the IOBM modulating effect. During an IOBM negative phase, which tends to coincide with La Niñ a events, the rainfall increase is far greater than the reduction during a positive IOBM phase, which tends to coincide with El Niñ o events. This modulation asymmetry is consistent with an asymmetry in the ENSO-rainfall teleconnection over Australia, in which the La Niñ a-rainfall teleconnection is stronger than the El Niñ o-rainfall teleconnection. This asymmetric ENSO-rainfall teleconnection ensures a higher coherence of northern Australia convective anomalies with La Niñ a or with a negative phase of the IOBM, hence a greater modification of the PSA pattern, underpinning the asymmetric modulating role of the IOBM.