  We develop the basic properties of $w$-simple-minded systems in
$(-w)$-Calabi-Yau triangulated categories for $w \geq 1$. The main result is a
reduction technique for negative Calabi-Yau triangulated categories. We show
that the theory of simple-minded systems exhibits striking parallels with that
of cluster-tilting objects. Our construction provides an inductive technique
for constructing simple-minded systems.
