The demand for high data rate and uniform throughput for cellular user terminals in the cell coverage leads to a new uplink coordinated multipoint (CoMP) transmission/reception technique proposed by the 3GPP LTE-A system. In this paper, we incorporate the recently proposed interference alignment (IA) techniques in uplink CoMP to improve system capacity by leveraging the full cooperation and information exchange via backhaul at the base stations. We propose a new iterative relaxed signal-to-leakage-plus-noise ratio (SLNR) IA criterion and further combine it with the maximum signal-to-interference-plus- noise ratio (SINR) IA criterion to form a mixed-criteria IA-aided CoMP scheme. The proposed new criteria exhibit excellent convergence behaviors and provide substantial performance gain for conventional CoMP, thanks to the joint processing advantage in centralized CoMP. The effectiveness of the proposed scheme is confirmed by computer simulations.