  We revisit the possibility of de Sitter vacua and slow-roll inflation in type
II string theory at the level of the classical two-derivative supergravity
approximation. Previous attempts at explicit constructions were plagued by
ubiquitous tachyons with a large $\eta$ parameter whose origin has not been
fully understood so far. In this paper, we determine and explain the tachyons
in two setups that are known to admit unstable dS critical points: an SU(3)
structure compactification of massive type IIA with O6-planes and an SU(2)
structure compactification of type IIB with O5/O7-planes. We explicitly show
that the tachyons are always close to, but never fully aligned with the
sgoldstino direction in the considered examples and argue that this behavior is
explained by a generalized version of a no-go theorem by Covi et al, which
holds in the presence of large mixing in the mass matrix between the sgoldstino
and the orthogonal moduli. This observation may also provide a useful stability
criterion for general dS vacua in supergravity and string theory.
