Compared to moving coil loudspeakers, carbon nanotube (CNT) loudspeakers are extremely lightweight and are capable of creating sound over a broad frequency range (1 Hz to 100 kHz). The thermoacoustic effect that allows for this non-vibrating sound source is naturally inefficient and nonlinear. Signal processing techniques are one option that may help counteract these concerns. Previous studies have evaluated a hybrid efficiency metric, the ratio of the sound pressure level at a single point to the input electrical power. True efficiency is the ratio of output acoustic power to the input electrical power. True efficiency data are presented for two new drive signal processing techniques borrowed from the hearing aid industry. Spectral envelope decimation of an AC signal operates in the frequency domain (FCAC) and dynamic linear frequency compression of an AC signal operates in the time domain (TCAC). Each type of processing affects the true efficiency differently. Using a 72 Wrms input signal, the measured efficiencies in the frequency range from 100 Hz to 10 kHz were 1.01 - 1083 E-6 and 1.26 - 388 E-6 percent for FCAC and TCAC, respectively. In addition, the effects of these processing techniques relative to sound quality were evaluated in terms of total harmonic distortion (THD). It was shown that although the different signal processing techniques affected the true efficiency, none of them increased the efficiency of the CNT loudspeaker to the level of current moving coil loudspeakers. Additionally, THD as the only sound quality metric is incomplete because these processing methods can be optimized for pure tones but highly distort complex signals like speech and music. Therefore, a sound quality metric for complex signals is needed. Overall, CNT loudspeakers show promise for specific applications where weight savings and complex geometries are required.