  We derive necessary criteria for the existence of classical, meta-stable, de
Sitter solutions in flux compactifications of type II supergravity down to
dimensions higher than four. We find that the possibilities in higher
dimensions are much more restricted than in four dimensions. The only models
that satisfy the criteria are derived from O6 compactifications to D=5,6 and O5
compactifications to D=5 and no meta-stable solutions can exist in dimensions
higher than six. All these models have in common that the compact dimensions
are negatively curved.
