This paper contrasts recent discussions of the theory of strengthening by coherent precipitates. The most important difference is in the assumed condition at maximum hardness. In one treatment, the maximum hardness is reached when dislocations first begin to loop precipitates, and is hence controlled by the largest particles in the precipitate size distribution. In the other treatment, the maximum hardness occurs when precipitates of average size are looped, and is hence controlled by the average precipitate size. More general theories of hardening by distributions of particles of different strength support the former treatment, but are incomplete. The experimental data is ambiguous. Experiments are needed to resolve the issue.