We analyse some redefinitions of the energy-momentum tensor of Classical Electrodynamics. Usually it has been considered as a necessary and sufficient criterion for redefining the energy-momentum tensor that the new tensor yields the "true" equation of motion of the electron, that is, the Lorentz-Dirac equation. We show that such a property is not sufficient. In fact, we study two specific examples in which the redefined energy momentum tensor yields a Lorentz-Dirac equation. However, in both cases the corresponding rate of emission associated to them is different to the well-known Larmor rate.