Prior work by the author established basic theorems relating the mechanical efficiency of an engine to its thermodynamic cycle, external pressure, and the effectiveness of its mechanism. That work treated the elementary single-workspace reciprocating piston heat engine. This paper extends the analysis to cover more complex engine types and heat pumps, including double-acting and split-workspace devices. Theorems are derived which allow best-possible estimates and broad comparisons of the overall performance of a large variety of thermomechanical machines. Examples from the field of Stirling engines illustrate the application of the main results.