Spectrum sharing is a key function to provide fairness allocation as well as service satisfaction across multiple users in cognitive radio networks. Even though spectrum sharing can benefit from spectrum handoff to enhance rate performance by switching from unavailable channels to available ones, the negative impact on handoff delay can cause significant service degradation. In this work, we present a hybrid spectrum sharing strategy that includes novel static and dynamic spectrum sharing algorithms based essentially on a rate compensation approach and adapted best fit algorithms. The static scheme is applicable for some specific network configurations where spectrum handoff is not necessary. Conversely, the dynamic scheme can benefit from spectrum handoff to increase the achieved rate and also compensate for the lost rate from the unavailable periods. These two sharing schemes are operated adaptively according to the current network environment. We compare our hybrid strategy with a fully dynamic one and an optimization framework. The proposed hybrid spectrum sharing demonstrates its effectiveness in terms of improving the overall service satisfaction and reducing the number of handoffs while the achieved rate is fulfilling compared to the optimal.