  We examine the structure of higher-derivative string corrections under a
cosmological reduction and make connection to generalized geometry and
T-duality. We observe that, while the curvature
$R^\mu{}_{\nu\rho\sigma}(\Omega_+)$ of the generalized connection with torsion,
$\Omega_+=\Omega+\frac{1}{2}H$, is an important component in forming T-duality
invariants, it is necessarily incomplete by itself. We revisit the tree-level
$\alpha'R^2$ corrections to the bosonic and heterotic string in the language of
generalized geometry and explicitly demonstrate that additional $H$-field
couplings are needed to restore T-duality invariance. We also comment on the
structure of the T-duality completion of tree-level $\alpha'^3R^4$ in the type
II string.
