  We show that the tree property, stationary reflection and the failure of
approachability at $\kappa^{++}$ are consistent with $\mathfrak{u}(\kappa) =
\kappa^+ < 2^\kappa$, where $\kappa$ is a singular strong limit cardinal with
the countable or uncountable cofinality. As a by-product, we show that if
$\lambda$ is a regular cardinal, then stationary reflection at $\lambda^+$ is
indestructible under all $\lambda$-cc forcings (out of general interest, we
also state a related result for the preservation of club stationary
reflection).
