Exciting new SPECT systems can be created by combining pinhole imaging with compact high-resolution gamma cameras. These new systems are able to solve the problem of the limited sensitivity-resolution trade-off that hampers contemporary small animal SPECT. The design presented here (U-SPECT-III) uses a set of detectors placed in a polygonal configuration and a cylindrical collimator that contains 135 pinholes arranged in nine rings. Each ring contains 15 gold pinhole apertures that focus on the centre of the cylinder. A non-overlapping projection is acquired via each pinhole. Consequently, when a mouse brain is placed in the central field-of-view, each voxel in the cerebrum can be observed via 130 to 135 different pinholes simultaneously. A method for high-resolution scintillation detection is described that eliminates the depth-of-interaction problem encountered with pinhole cameras, and is expected to provide intrinsic detector resolutions better than 150 microm. By means of simulations U-SPECT-III is compared to a simulated dual pinhole SPECT (DP-SPECT) system with a pixelated array consisting of 2.0 x 2.0 mm NaI crystals. Analytic calculations indicate that the proposed U-SPECT-III system yields an almost four times higher linear and about sixty times higher volumetric system resolution than DP-SPECT, when the systems are compared at matching system sensitivity. In addition, it should be possible to achieve a 15 up to 30 times higher sensitivity with U-SPECT-III when the systems are compared at equal resolution. Simulated images of a digital mouse-brain phantom show much more detail with U-SPECT-III than with DP-SPECT. In a resolution phantom, 0.3 mm diameter cold rods are clearly visible with U-SPECT-III, whereas with DP-SPECT the smallest visible rods are about 0.6-0.8 mm. Furthermore, with U-SPECT-III, the image deformations outside the central plane of reconstruction that hamper conventional pinhole SPECT are strongly suppressed. Simulation results indicate that future pinhole SPECT systems are likely to bring about significant improvements in radio-molecular imaging of small animals.