Satellites on low-Earth orbit usually have scarce opportunities to contact ground stations. Resulting contact windows define the satellite access time, which depends on the satellite’s orbit and the ground facilities distribution on Earth’s surface. In recent years, the cost of constructing and launching small satellites has decreased dramatically, introducing a new possibility for space agencies: to take into consideration small relay satellites to increase access times. This paper presents Maximum Asset Accessibility Algorithm (M3A), a novel methodology based on simulated annealing parametric search to design satellite missions with maximum access times. Orbit constraints and possible locations for ground facilities are considered on the task of selecting the optimal combination of orbital parameters for the assets of a space mission. Results show that the use of M3A drastically reduces the required design time, while providing parameters of similar quality than those obtained by processor-demanding brute force search.