  As an alternative to the covariant Ostrogradski method, we show that
higher-derivative relativistic Lagrangian field theories can be reduced to
second differential-order by writing them directly as covariant two-derivative
theories involving Lagrange multipliers and new fields. Notwithstanding the
intrinsic non-covariance of the Dirac's procedure used to deal with the
constraints, the Lorentz invariance is recovered at the end. We develope this
new setting for a simple scalar model and then its applications to generalized
electrodynamics and higher-derivative gravity are outlined. This method is
better suited than Ostrogradski's for a generalization to 2n-derivative
theories.
