To realize Quantitative MRI (QMRI) with clinically acceptable scan time, acceleration factors achieved by conventional parallel imaging techniques are often inadequate. Further acceleration is possible using model-based reconstruction. We propose a theoretical metric called TEUSQA: Time Efficiency for UnderSampled QMRI Acquisitions to inform sequence design and sample pattern optimisation. TEUSQA is designed for a particular class of reconstruction techniques that directly estimate tissue parameters, possibly using prior information to regularize the estimation. TEUSQA can be used to evaluate undersampling patterns for multi-contrast QMRI sequences targeting any tissue parameter. To verify the time efficiency predicted by TEUSQA, we performed Monte Carlo simulations and an accelerated parameter mapping with two sequences (Inversion prepared fast spin echo for T1 and T2 mapping and 3D GRASE for T2 and B0 inhomogeneity mapping). Using TEUSQA, we assessed several ways to generate undersampling patterns in silico, providing insight into the relation between sample distribution and time efficiency for different acceleration factors. The time efficiency predicted by TEUSQA was within 15% of that observed in the Monte Carlo simulations and the prospective acquisition experiment. The assessment of undersampling patterns showed that a class of good patterns could be obtained by low-discrepancy sampling. We believe that TEUSQA offers a valuable instrument for developers of novel QMRI sequences pushing the boundaries of acceleration to achieve clinically feasible protocols. Finally, we applied a time-efficient undersampling pattern selected using TEUSQA for a 32-fold accelerated scan to map T1 & T2 mapping of a healthy volunteer.