Thallium bromide (TlBr) has attracted attention as an exceptional radiation detector material. Due to its high atomic number (81 for Tl, 35 for Br) it has excellent stopping power for hard X-ray and gamma rays and due to its high bandgap (2.7 eV) its operation requires no or only modest cooling. Promising energy resolutions have been demonstrated with detectors fabricated from high-purity samples (3.3 keV for 60 keV photons). These properties make TlBr the material of choice for hard X-ray imaging spectrometers in applications where small weight and/or size is important (e.g. space astrophysics and nuclear medicine). The charge response and spectroscopic performance of a semiconductor imaging array depend not only on material properties but on the pixel properties as well. It has been demonstrated, for instance, that the ratio between pixel size and thickness of the detector is an important factor for the charge response. This is known as the small-pixel or near-field effect. In this paper we investigate the optimization of TlBr pixel properties in a broader context, taking into account material properties (electron and hole mobility, diffusion and trapping), fabrication details and the specific energy range of application, with a view to optimizing both the response and energy resolution.