Record low austral winter rainfall totals over southwest Western Australia (SWWA) in 2010 saw a continuation of the multidecade-long winter drought plaguing the region. During this season, the highest recorded positive Southern Annular Mode (SAM) value was measured, adding weight to an association of a positive SAM with anomalously low SWWA winter rainfall (SWR), and vice-versa. However, such a SAM-SWR teleconnection has been recently questioned. Using observational data in the post-1979 satellite era, it is shown that such a SAM influence does exist. This coherence is confirmed with 1150 years of modelled 20th century SWR anomalies and SAM values from 23 climate models, showing that a nonlinear impact operates: the influence from a negative SAM is greater than that from a positive SAM. This explains why a small positive shift in the SAM can cause a large SWR reduction, as has been observed. A further test shows that models with a greater positive SAM trend systematically produce a greater future SWR reduction. As all climate models project an increase in the SAM these results suggest that as global warming continues unabated, SWWA winter droughts will be more persistent as atmospheric conditions become more unfavourable for drought-breaking rains.