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Coordinated multi-point transmission (CoMP) joint processing (CoMP-JP) is a promising technique for supporting high spectral efficiency in future cellular systems. However, this technique requires high-capacity backhaul links for connecting multiple base stations (BSs), which leads to high deployment costs. CoMP coordinated beamforming (CoMP-CB) needs less backhaul capacity, but with lower maximal multiplexing gain. In this paper, we study downlink CoMP strategies with limited-capacity backhaul. We start by investigating the optimal interference-free transmission strategy under backhaul rate constraints, where only a part of the data is shared among the BSs. We then study soft and hard switching between the CoMP-JP and CoMP-CB modes. Finally, a closed-form semi-dynamic distributed hard switching scheme is proposed, which depends on the local large-scale channel gains of the users. Simulation results show that both the soft and hard mode switching transmission perform closely to the optimal strategy and outperform the single-mode CoMP transmission especially when the backhaul capacity is very limited.