The energy efficiency of comminution processes is very low based on the energy required to generate new fracture surface area relative to the mechanical (strain) energy input. However, the maximum ideal limiting efficiency E-Limit, against which actual efficiencies may be compared is unknown. Therefore, theoretical analyses were undertaken to determine E-Limit for a compressive loading comminution machine based on the stress state in a single particle containing a central crack (flaw). The analyses show that E-Limit increases with increasing Poisson's ratio nu, having values of similar to 5%, similar to 7.5% and similar to 9% at nu similar to 0, similar to 0.2 and similar to 0.39, respectively. Actual energy efficiencies, E-B, expressed in terms of the energy required to create new fracture surface area relative to the work input, using standard Bond work index values, are lower in the range <1% to similar to 2%. The relative efficiency ratio E-B/E-Limit varies from similar to 3% to similar to 26%, depending on the mineral, and is considered to be a more useful (practical) measure of efficiency because it gives a better assessment of behaviour relative to the limiting situation. It is concluded from the EB/E-Limit ratios that the potential exists to improve comminution efficiencies by two or three times. Possible methods of achieving this are discussed. (C) 2007 Elsevier Ltd. All rights reserved.