Strongly nonlinear amplifiers have lower implementation complexity, together with much higher amplification efficiency than linear amplifiers. However, they are only recommendable when the signals at their input have very low envelope fluctuations, something that in general is incompatible with signals with high spectral efficiency (i.e. employing high-order constellations). It is proved, although, that spectral efficient M-ary constellations can be decomposed as a sum of several OQPSK signals that can be amplified separately, thus bringing a new life for this modulation scheme. Constant- envelope OQPSK-type signals can be obtained using its equivalent minimum shift keying (MSK) representation, but don't possess the required compact spectrum close to the minimum Nyquist frequency. This can only be achieved by employing narrowband Nyquist filters, which on the other hand causes the signal's envelope to fluctuate. Considering that, this paper proposes a ring-type magnitude modula- tion (RMM) method for narrowband offset quadrature phase shift keying (OQPSK) signals that considerably reduces its envelope fluctuations with- out spreading the transmitted signal's spectrum. Simulation results show that the reduction of the signal's dynamic range and peak-to-average power ratio (PAPR) allows the use of highly efficient, nonlinear saturated high power amplifiers (HPAs) without spreading the signal's spectrum and with minimum bit error rate (BER) performance degradation.