The small-scale open and direct solar thermal Brayton cycle with recuperator has several advantages, including low cost, low operation and maintenance costs and it is highly recommended. The main disadvantages of this cycle are the pressure losses in the recuperator and receiver, turbomachine efficiencies and recuperator effectiveness, which limit the net power output of such a system. The irreversibilities of the solar thermal Brayton cycle are mainly due to heat transfer across a finite temperature difference and fluid friction. In this paper, thermodynamic optimisation is applied to concentrate on these disadvantages in order to optimise the receiver and recuperator and to maximise the net power output of the system at various steady-state conditions, limited to various constraints. The effects of wind, receiver inclination, rim angle, atmospheric temperature and pressure, recuperator height, solar irradiance and concentration ratio on the optimum geometries and performance were investigated. The dynamic trajectory optimisation method was applied. Operating points of a standard micro-turbine operating at its highest compressor efficiency and a parabolic dish concentrator diameter of 16 m were considered. The optimum geometries, minimum irreversibility rates and maximum receiver surface temperatures of the optimised systems are shown. For an environment with specific conditions and constraints, there exists an optimum receiver and recuperator geometry so that the system produces maximum net power output.