The Extended Reference Region Model (ERRM) can quantify tumour perfusion without needing an arterial input function and includes a vascular term to account for the plasma volume. The addition of the vascular term also leads to larger variability in the estimated parameters. This study notes that one of the ERRM fitting parameters should be the same for all voxels. A two-fit approach is proposed that takes advantage of this constraint to reduce the number of fitting parameters from four to three. Evaluation in simulation and in-vivo found that the proposed two-fit approach resulted in a substantial decrease in variability for KTrans and kep estimates.