Some applications of thermoacoustics will require high power density to reduce the cost and size of the hardware needed for a given total power. Such high power density can be reached by using high acoustic amplitudes, but this leads to significant differences between the actual operation and predictions based on the acoustic approximation. To date, all such differences have resulted in reduced efficiency. Experimental results for several thermoacoustic engines operated with acoustic pressure amplitudes near 10% of mean pressure will be presented. Causes of deviation from acoustic-approximation predictions, including entrance effects, turbulence, and harmonic content, will be discussed. Experimental and theoretical approaches to understanding these deviations will be proposed.