Quantification of the spin-lattice relaxation time, T1, of tissues is important for characterization of tissues in clinical magnetic resonance imaging (MRI). In T1 mapping, T1 values are estimated from a set of T1-weighted MRI images. Due to the limited spatial resolution of the T1-weighted images, one voxel might consist of two tissues, causing partial volume effects (PVE). In conventional mono-exponential T1 estimation, these PVE result in systematic errors in the T1 map. To account for PVE, single-voxel bi-exponential estimators have been suggested. Unfortunately, in general, they suffer from low accuracy and precision. In this work, we propose a joint multi-voxel bi-exponential T1 estimator (JMBE) and compare its performance to a single-voxel bi-exponential T1 estimator (SBE). Results show that, in contrast to the SBE, and for clinically achievable single-voxel SNRs, the JMBE is accurate and efficient if four or more neighboring voxels are used in the joint estimation framework. This illustrates that, for clinically realistic SNRs, accurate results for quantitative biexponential T1 estimation are only achievable if information of neighboring voxels is incorporated.