Non-contiguous orthogonal frequency-division multiplexing (OFDM) is a promising technique for cognitive radio systems. The secondary users transmit on the selected subcarriers to avoid the frequencies being used by the primary users. However, the out-of-band power (OBP) of the OFDM-modulated tones induces interference to the primary users. Another major drawback of OFDM-based system is their high peak-to-average power ratio (PAPR). In this paper, algorithms are proposed to jointly reduce the OBP and the PAPR for non-contiguous OFDM based on the method of alternating projections onto convex sets. Several OFDM subcarriers are selected to accommodate the adjusting weights for OBP and PAPR reduction. The frequency-domain OFDM symbol is projected onto two convex sets that are defined according to the OBP requirements and the PAPR limits. Each projection iteration solves a convex optimization problem. The projection onto the set constrained by the OBP requirement can be calculated using an iterative algorithm which has low computational complexity. Simulation results show good performance of joint reduction of the OBP and the PAPR. The proposed algorithms converge quickly in a few iterations.