This work reports a Class-E pulse-width modulated RF power amplifier that uses multilevel discrete supply modulation for base station applications. This work quantifies the efficiency roll-off in multilevel PAs and proposes that pulse-width modulated (PWM) class-E PAs offer the best efficiency roll-off and dynamic range, based on the efficiency profile with power back-off (PBO). The presented technique significantly extends the PBO dynamic range of PWM PAs over prior state-of-the-art solutions. A proof of concept watt-level class-E PA is designed using a GaN HEMT and exhibits more than 65% efficiency at 15dB PBO. This design extends the dynamic range of a PWM class-E PA to more than 6dB for a 50 to 30 percent duty cycle variation, and offers an efficiency roll-off of less than 4% per dB. The proposed circuit demonstrates an increasing average drain efficiency with power back-off when reducing the PA supply voltage.