The MOLLI sequence for myocardium T1 quantification is widely applied in the clinical setting. The standard 3-parameter fitting algorithm allows a high precision in the T1 estimates but it comes at the cost of a low accuracy. The accuracy can be improved using the instantaneous signal loss (InSiL) approximation method for signal fitting. In this work we evaluated the robustness of the InSiL algorithm when fat also contributes to the signal. The results show that InSiL enables to increase the accuracy of the MOLLI sequence even in the presence of partial volume effects due to fat.