This paper considers the use of the linear amplification with nonlinear components (LINC) technique for the power amplification of spectrally compact offset quadrature phase shift keying (OQPSK) signals allowing the use of highly efficient, low cost, and strongly nonlinear high power amplifiers (HPAs). However, the performance of the LINC signal separation and power combining procedures decreases with the rise of the signal’s peak-to-average power ratio (PAPR). A new ringtype magnitude modulation (RMM) method is proposed for OQPSK signals that limits both its maximum and minimum complex envelope excursions avoiding zero crossings, without spreading the transmitted signal’s spectrum. The performance results show that bandlimited OQPSK signals whose envelope have low fluctuations produce LINC components with a narrower spectrum, with a considerable impact on the LINC transmitter regardless of the type of combiner chosen: when using a passive/matched combiner, the transmitter’s power efficiency is significantly increased without spreading the combined signal’s spectrum; for the highly efficient non-linear Chireix combiner there is a reduction of the amount of spectral leakage produced by nonlinearly combining the LINC signal components. Finally, an iterative decoding scheme is also proposed, which employs estimates of the received symbols’ RMM coefficients to compensate the RMM distortion.