Homogenous alkali-catalysed biodiesel production from waste cooking oil (WCO) requires acid-catalysed pretreatment steps due to high free fatty acid (FFA) contents. This study investigated strategies to obtain high yields of fatty acid methyl esters (FAME) from one-step base-catalysed transesterification of WCO containing high levels of free fatty acids (up to 5.5 wt%) and 3 wt% of water by altering operating conditions. About 98% FAME yield in homogeneous NaOCH3-catalysed transesterification was obtained within 5 min reaction time at methanol to WCO molar ratios of 12: 1-18: 1 and 3 wt% catalyst loading for WCO containing 1.53% FFA and 0.12 wt % water. It was found that high molar ratios of methanol to oil (> 6: 1) could prevent saponification. At 5.5 wt% FFA and 3 wt% water contents, >= 96.5% FAME yield was achieved at 18: 1M ratio of methanol to WCO within 5 min compared to only 62.8 +/- 1.2% for a molar ratio of 6:1. Mathematical modelling (MATLAB) was used to predict FAME yields at various conditions and validated using experimental data. Sets of conditions identified in this study can be used to rapidly produce biodiesel from low quality triglyceride sources in a single step base-catalysed process.