  A novel nonlinear electrodynamics (NLE) model with two dimensionful
parameters is introduced and investigated. Our model obeys the Maxwellian limit
and exhibits behaviour similar to the Born-Infeld Lagrangian in the weak field
limit. It is shown that the electric field of a point charge in this model has
a definite maximum value. Thus, the self-energy of the point charge is finite.
The phenomenon of vacuum birefringence is found to occur in the presence of an
external uniform electric field. Causality and unitarity conditions for all
background electric fields hold, whereas, for magnetic fields, a restricted
domain of validity is found. Moreover, a minimal coupling of Einstein's General
Relativity (GR) with this NLE results in solutions of regular black holes or
naked singularities, depending on whether the source is a nonlinear magnetic
monopole or an electric charge, respectively.
