  We discuss the possibility to construct supergravity models with a single
superfield describing inflation as well as the tiny cosmological constant $V
\sim 10^{{-120}}$. One could expect that the simplest way to do it is to study
models with a supersymmetric Minkowski vacuum and then slightly uplift them.
However, due to the recently proven no-go theorem, such a tiny uplifting cannot
be achieved by a small modification of the parameters of the theory. We
illustrate this general result by investigation of models with a single chiral
superfield recently proposed by Ketov and Terada. We show that the addition of
a small constant or a linear term to the superpotential of a model with a
stable supersymmetric Minkowski vacuum converts it to an AdS vacuum, which
results in a rapid cosmological collapse. One can avoid this problem and uplift
a supersymmetric Minkowski vacuum to a dS vacuum with $V_{0}\sim 10^{-120}$
without violating the no-go theorem by making these extra terms large enough.
However, we show that this leads to a strong supersymmetry breaking in the
uplifted vacua.
