In this paper, we analyze the achievable capacity of the secondary service for overlay and underlay access strategies. We then propose a novel mixed access strategy in which in contrast to the underlay strategy, the secondary service transmits during the idle periods without considering the interference threshold constraint. In contrast to the overlay strategy, mixed strategy makes transmission during the busy periods with a probability p(a) subject to satisfying the interference threshold constraint. Parameter p(a) is a secondary service parameter, which can be adjusted based on the spectrum status. Moreover, we show that the secondary service can adjust pa to select appropriate access strategy with the objective of maximizing the achieved capacity based on the interference at the secondary service receiver, I, imposed by the primary service transmitter. The proposed spectrum-sharing technique developed in this paper based on I significantly reduces the system complexity comparing to the system in which for spectrum sharing, the imposed interference at the primary receiver is required. We further suggest a simple power allocation scheme for the mixed strategy that its achieved capacity is very close to the maximum achievable capacity of the secondary service.