  We suggest a new spin-4 self-dual model (parity singlet) and a new spin-4
parity doublet in $D=2+1$. They are of higher order in derivatives and are
described by a totally symmetric rank-4 tensor without extra auxiliary fields.
Despite the higher derivatives they are ghost free. We find gauge invariant
field combinations which allow us to show that the canonical structure of the
spin-4 (spin-3) models follows the same pattern of its spin-2 (spin-1)
counterpart after field redefinitions. For $s=1,2,3,4$, the spin-$s$ self-dual
models of order $2s-1$ and the doublet models of order $2s$ can be written in
terms of three gauge invariants. The cases $s=3$ and $s=4$ suggest a restricted
conformal higher spin symmetry as a principle for defining linearized
topologically massive gravity and linearized "New Massive Gravity" for
arbitrary integer spins. A key role in our approach is played by the fact that
the Cotton tensor in $D=2+1$ has only two independent components for any
integer spin.
