Presently used clinical brain SPECT suffers from limited spatio-temporal resolution. Here we investigate the feasibility of high-resolution and high-sensitivity full-ring multi-pinhole brain SPECT (MP-SPECT). Using an analytical model we optimized pinhole-detector geometries of MP-SPECT for different detector intrinsic resolutions R(i). System resolution and sensitivity of optimized MP-SPECT were compared to conventional clinical SPECT. The comparison of the system resolution of different systems was done at matched sensitivity, which was achieved by tuning pinhole diameters. Similarly, sensitivities were compared at matched system resolution. For MP-SPECT that uses detectors with intrinsic resolutions of 4 mm > R(i) 0.5 mm a sensitivity can be achieved that is 6.0 times higher than the sensitivity of conventional dual-head SPECT systems with parallel-hole collimators (DualPar), while system resolution can be improved by a factor of 2.4. To achieve these improvements a large detector-to-collimator distance is needed. In contrast, for detectors with intrinsic resolutions <0.2 mm, it is beneficial to place the detectors close to the pinholes, resulting in a high number of de-magnified projections. For a detector intrinsic resolution of 0.05 mm, a 14.5-fold improvement in sensitivity and a 3.8-fold improvement in system resolution compared to DualPar is predicted. Furthermore, we found that for optimized MP-SPECT the sensitivity scales proportionally to system resolution squared, with the proportionality constant depending on R(i). From our sensitivity-system resolution trade-off equations we deduced that MP-SPECT with an ideal detector (R(i) --> 0) can have a system resolution that is 2.0 times better than optimized MP-SPECT with a conventional detector (R(i) approximately 3 mm). The high performance of optimized MP-SPECT may open up completely new molecular imaging applications.