This paper presents a high payload data-hiding scheme for audio signals following the OFDM concept. It is based on changing the phase component of the audio signal via a reduced-arc M-order Phase Shift Key- ing (MPSK) modulator on selected frequency samples of the audio signal. This approach allows the data- hiding payload and perceptual distortion to be controlled by the number of altered frequency compo- nents of the audio signal and the severity of this alteration. The data-hiding payload can be estimated a priori independently of the audio signal features. In addition, due to the relation of the proposed scheme with the traditional use of MPSK modulation, the BER of the encoded data is analytically derived, there- fore, it is known in advance. This allows the transmission of reliable hidden data, in contrast to previous works. Results obtained with representative test cases show that the proposed algorithm provides an increase of one order of magnitude in data payload compared with state-of-the-art works.