  We consider both generalized Born-Infeld and Exponential Electrodynamics. The
field-energy of a point-like charge is finite only for Born-Infeld-like
Electrodynamics. However, both Born-Infeld-type and Exponential Electrodynamics
display the vacuum birefringence phenomenon. Subsequently, we calculate the
lowest-order modifications to the interaction energy for both classes of
Electrodynamics, within the framework of the gauge-invariant path-dependent
variables formalism. These are shown to result in long-range ($1/r^5$- type)
corrections to the Coulomb potential. Once again, for their non-commutative
versions, the interaction energy is ultraviolet finite.
