Class A/B
Class A/B amplifiers are a compromise. They still use a bias voltage, but only to lift the crossover a little away from zero. That reduces much of the distortion inherent in Class B, while avoiding the extreme inefficiency of Class A. Class A/B remains the most common design method for high fidelity amplifiers and with modern careful design they often deliver magnificent performance.
There are lots of design choices available to designers, including the level of the bias voltage. The brand Moon by Simaudio, for example, sets its bias voltage relatively high so that the first five watts of power in its higher end models are pure Class A.