  We initiate a study of corrections to the K\"ahler potential of
$\mathcal{N}=1$ type II/F-theory compactifications that arise from curvature
terms in the action of D-branes and orientifold planes. We first show that a
recently proposed correction to the K\"ahler coordinates, which was argued to
appear at order $\alpha^{\prime 2}g_s$ and be proportional to the intersection
volume of D7-branes and O7-planes, is an artifact of an inconvenient field
basis in the dual M-theory frame and can be removed by a field redefinition of
the 11D metric. We then analyze to what extent curvature terms in the DBI and
WZ action may still lead to corrections of a similar kind and identify two
general mechanisms that can potentially modify the volume dependence of the
K\"ahler potential in the presence of D-branes and O-planes. The first
mechanism is related to an induced Einstein-Hilbert term on warped brane
worldvolumes, which leads to a shift in the classical volume of the
compactification manifold. The resulting corrections are generic and can appear
at one-loop order on branes and O-planes of various dimensions and for
configurations with or without intersections. We discuss in detail the example
of intersecting D7-branes/O7-planes, where a correction can appear already at
order $\alpha^{\prime 2}g_s^2$ in the K\"ahler potential. Due to an extended
no-scale structure, however, it is then still subleading in the scalar
potential. We also discuss a second mechanism, which is due to an induced
D3-brane charge in the WZ action of D7-branes. Contrary to the first type of
corrections, it appears at open string tree-level and shifts the definition of
the K\"ahler coordinates in terms of the classical volume but leaves the volume
itself uncorrected. Our work has implications for moduli stabilization and
model building and suggests interesting generalizations to F-theory.
