  We use compatibility of the $D$-dimensional effective actions for diagonal
metric and for dilaton with the T-duality when theory is compactified on a
circle, to find the the $D$-dimensional couplings of curvatures and dilaton as
well as the higher derivative corrections to the $(D-1)$-dimensional Buscher
rules at orders $ \alpha' $ and $\alpha'^2$. We observe that the T-duality
constraint on the effective actions fixes the covariant effective actions at
each order of $\alpha'$ up to field redefinitions and up to an overall factor.
Inspired by these results, we speculate that the $D$-dimensional effective
actions at any order of $\alpha'$ must be consistent with the standard Buscher
rules provided that one uses covariant field redefinitions in the corresponding
reduced $(D-1)$-dimensional effective actions. This constraint may be used to
find effective actions at all higher orders of $\alpha'$.
