This paper proposes a partial transmit sequences (PTS)-based PAPR reduction method and a phase factor estimation method without side information for OFDM systems with QPSK and 16QAM modulation. In the transmitter, an iterative algorithm that minimizes the p-norm of a transmitted signal determines phase factors to reduce PAPR. Unlike conventional methods, the phase factors are allowed to take continuous values in a limited range. In the receiver, the phase factor is blindly estimated by evaluating the phase differences between the equalizer's output and its closest constellation points. Simulation results show that the proposed PAPR reduction method is more computationally efficient than the conventional PTS. Moreover, the combined use of the two proposed methods achieves a satisfactory tradeoff between PAPR and BER by limiting the phase factors properly.