  In an earlier paper, the second author resolved a question of McDuff by
constructing a non-Hamiltonian symplectic circle action on a closed, connected
six-dimensional symplectic manifold with exactly 32 fixed points. In this
paper, we improve on this example by reducing the number of fixed points. More
concretely, we construct a non-Hamiltonian symplectic circle action on a
closed, connected six-dimensional symplectic manifold with exactly $2k$ fixed
points for any $k \geq 5$.
