The language of hurricane intensity theory is used to assess the important controls and resolution dependence of intensity in axisymmetric numerical models. Specifically, the energetically-based maximum intensity theory (E-MPI) of K. Emanuel is used since it has many dynamical elements and is constructed solely on axisymmetric principles. Certain elements of the E-MPI theory are found difficult to apply to model output. One example is the value of boundary layer relative humidity, since the tendency of one cloud-resolving axisymmetric model (the Rotunno and Emanuel 1987 model) is to saturate the lowest grid level. In this case, the assumptions of E-MPI can be relaxed and a point in the derivation can be found where relative humidity does not appear. This earlier point in the derivation is not a new a priori MPI, but rather a local diagnosis of the assumptions used to derive E-MPI. Discrepancies between the assumptions of E-MPI and the modeled intensity of the storm point to the important physical processes in the model that regulate intensity. We see this work as a first step toward analyzing the processes that regulate intensity in more realistic three-dimensional cloud-resolving models.