  In 1967, Chillingworth proved that all convex simplicial 3-balls are
collapsible. Using the classical notion of tightness, we generalize this to
arbitrary manifolds: We show that all tight simplicial 3-manifolds admit some
perfect discrete Morse function. We also strengthen Chillingworth's theorem by
proving that all convex simplicial 3-balls are non-evasive. In contrast, we
show that many non-evasive 3-balls are not convex.
