  Gauge fields are special in the sense that they are invariant under gauge
transformations and \emph{``ipso facto''} they lead to problems when we try
quantizing them straightforwardly. To circumvent this problem we need to
specify a gauge condition to fix the gauge so that the fields that are
connected by gauge invariance are not overcounted in the process of
quantization. The usual way we do this in the light-front is through the
introduction of a Lagrange multiplier, $(n\cdot A)^{2}$, where $n_{\mu}$ is the
external light-like vector, i.e., $n^{2}=0$, and $A_{\mu}$ is the vector
potential. This leads to the usual light-front propagator with all the ensuing
characteristics such as the prominent $(k\cdot n)^{-1}$ pole which has been the
subject of much research. However, it has been for long recognized that this
procedure is incomplete in that there remains a residual gauge freedom still to
be fixed by some ``ad hoc'' prescription, and this is normally worked out to
remedy some unwieldy aspect that emerges along the way. In this work we propose
\emph{two} Lagrange multipliers with distinct coefficients for the light-front
gauge that leads to the correctly defined propagator with no residual gauge
freedom left. This is accomplished via $(n\cdot A)^2+(\partial \cdot A)^2$
terms in the Lagrangian density. These lead to a well-defined and exact though
Lorentz non invariant propagator.
