Bias correction is an important step for achieving accurate and precise parameter quantification in MRI. Residual T2*-weighting in quantitative proton density maps estimated from short echo time FLASH images is often considered negligible, despite the potential bias. Using the hMRI toolbox, we analyse simulated FLASH-based multiparameter mapping datasets with variable noise levels. Using the quantitative maps on which the simulations are based as a gold standard, we quantified the bias caused by residual T2*-weighting. Furthermore, we evaluated a number of estimation methods in terms of their sensitivity and/or effectiveness at correcting this T2*-weighting bias, and in terms of their robustness to background noise.