Pinhole collimation is used in SPECT for small-animal imaging and more recently for human Cardiac SPECT. In pinhole collimation for SPECT, the system resolution function depends on the magnification, pinhole-diameter, the detector intrinsic resolution and depth of interaction. The magnification and the depth of interaction change with the surface geometry. Factors such as resolution and surface area can be optimized by changing the shape of the detector. The goal of this work is to formulate and optimize the detector surface geometry to minimize the system resolution, keeping a constant base of the detectors fitted on the similar base-radius pinhole collimator, given surface area constraints. We formulate the system resolution as a function of a height-function h, varying with ray-angle. We approximate this height function as a quadratic curve. We can then find the parameters of the quadratic that will minimize the resolution function subject to surface area constraints. Note once the resolution is optimized, it can be traded with sensitivity (if so desired) by opening the pinhole diameter. Our preliminary NCAT phantom reconstruction on the optimized and flat detectors placed on pinholes shows sensitivity gain factor of 1.6 for similar resolution. Specifically, our results for NCAT reconstruction of GATE simulations on spherical and flat detectors placed on pinholes corroborates our idea that using a curved detector behind a pinhole instead of a flat-one one would obtain significant advantages of resolution or dose-reduction, on an already ultra-fast system.