  We ask to what extent are the higher-derivative corrections of string theory
constrained by T-duality. The seminal early work by Meissner tests T-duality by
reduction to one dimension using a distinguished choice of field variables in
which the bosonic string action takes a Gauss-Bonnet-type form. By analyzing
all field redefinitions that may or may not be duality covariant and may or may
not be gauge covariant we extend the procedure to test T-duality starting from
an action expressed in arbitrary field variables. We illustrate the method by
showing that it determines uniquely the first-order $\alpha'$ corrections of
the bosonic string, up to terms that vanish in one dimension. We also use the
method to glean information about the ${\cal O}(\alpha'^2)$ corrections in the
double field theory with Green-Schwarz deformation.
