A low peak-to-average-power-ratio (PAPR) modulation technique is proposed for discrete Fourier transform precoded orthogonal frequency division multiple access (DFT-precoded-OFDMA) systems. This technique reduces the PAPR by introducing a phase rotation between successive modulation symbols along with partial response (PR) precoding before feeding the data to a DFT-precoded-OFDMA modulator. The PAPR reduction is shown to be quite significant for amplitude-shift-keying systems based on real constellations employing π/2 phase rotation. In particular, for the special case of binary modulation, the combination of phase rotation and PR precoding produces a signal with low amplitude variations. We show that the class of PR precoders obtained by sampling the linearised Gaussian-minimum-shift-keying pulse provides low PAPR and a small degradation in bit-error-rate (BER) performance. In particular, the widely linear minimum-mean-square-error (WL-MMSE) estimation and WL MMSE decision feedback equaliser (WL MMSE-DFE) methods that jointly filter the signal and its complex conjugate are shown to be useful in mitigating the additional intersymbol interference introduced by the PR precoder. The BER performance is comparable with that of conventional DFT-precoded-OFDMA systems employing conventional equalisers. The proposed technique is also suitable for reducing the PAPR of Q-ary phase-shift-keying systems based on complex constellations employing a phase rotation of π/Q. Introduction of Type A-2 PR precoder that is obtained from the linearised Gaussian-minimum-shift-keying pulse reduces the PAPR by 3.0 dB for quadrature phase-shift keying, and 2.5 dB reduction is observed for Q-ary phase-shift keying with Q ≥ 8. The intersymbol interference created by the PR precoder causes bit-error-rate degradation in the range of 2.0-2.5 dB when conventional MMSE-DFE receiver is used for symbol detection. Copyright © 2012 John Wiley & Sons, Ltd.