  Double Field Theory is a manifestly T-duality invariant formulation of string
theory in which the effective theory at any order of $\alpha'$ is invariant
under global $O(D,D)$ transformations and ought to be invariant under gauge
transformations which receive $\alpha'$-corrections. On the other hand, the
effective theory in the usual $D$-dimensional formulation of string theory is
manifestly gauge invariant and ought to be invariant under T-duality
transformations which receive $\alpha'$-corrections. We speculate that the
combination of these two constraints may fix both the $2D$-dimensional and the
$D$-dimensional effective actions without knowledge of the
$\alpha'$-corrections of the gauge and the T-duality transformations.
  In this paper, using generalized fluxes, we construct arbitrary
$O(D,D)$-invariant actions at orders $\alpha'^0$ and $\alpha'$, and then
dimensionally reduce them to the $D$-dimensional spacetime. On the other hand,
at these orders, we construct arbitrary covariant $D$-dimensional actions.
Constraining the two $D$-dimensional actions to be equal up to non-covariant
field redefinitions, we find that both actions are fixed up to overall factors
and up to field redefinitions.
