  There are three self-dual models of massive particles of helicity +2 (or -2)
in $D=2+1$. Each model is of first, second, and third-order in derivatives.
Here we derive a new self-dual model of fourth-order, $\cL {SD}^{(4)}$, which
follows from the third-order model (linearized topologically massive gravity)
via Noether embedment of the linearized Weyl symmetry. In fact, each self-dual
model can be obtained from the previous one $ \cL {SD}^{(i)} \to \cL
{SD}^{(i+1)}, i=1,2,3$ by the Noether embedment of an appropriate gauge
symmetry, culminating in $\cL {SD}^{(4)}$. The new model may be identified with
the linearized version of $\cL {HDTMG} = \epsilon^{\mu\nu\rho}
\Gamma_{\mu\gamma}^\epsilon (\p_\nu\Gamma_{\epsilon\rho}^\gamma +
(2/3)\Gamma_{\nu\delta}^\gamma \Gamma_{\rho\epsilon}^\delta) /8 m +
\sqrt{-g}(R_{\mu\nu} R^{\nu\mu} - 3 R^2/8) /2 m^2 $. We also construct a master
action relating the third-order self-dual model to $\cL {SD}^{(4)}$ by means of
a mixing term with no particle content which assures spectrum equivalence of
$\cL {SD}^{(4)}$ to other lower-order self-dual models despite its pure higher
derivative nature and the absence of the Einstein-Hilbert action. The relevant
degrees of freedom of $\cL {SD}^{(4)}$ are encoded in a rank-two tensor which
is symmetric, traceless and transverse due to trivial (non-dynamic) identities,
contrary to other spin-2 self-dual models. We also show that the Noether
embedment of the Fierz-Pauli theory leads to the new massive gravity of
Bergshoeff, Hohm and Townsend.
