This paper examines the sign and size-dependent asymmetry in wholesale petrol and diesel prices in the long and short run across seven major distribution centres in Australia using daily data from 1 January 2004 to 18 November 2022. This study adopts a composite threshold mean model that is augmented with an asymmetric power autoregressive conditional heteroskedasticity (APARCH) model or an exponential general autoregressive conditional heteroskedastic (EGARCH) model to capture volatility clustering in high-frequency data. Inter alia, the results reveal that the long-run (adjustment) asymmetry is more widespread for unleaded petrol prices than diesel prices. Melbourne and Perth are the only two outport terminals that do not exhibit short- or long-run asymmetry for both diesel and petrol. In terms of the adjustment asymmetry, terminal gate prices for petrol in Darwin, Hobart, and Sydney are the least competitive, whereas the opposite is true for Adelaide, Brisbane, and Perth.