  A $PT$-symmetric dimer is a two-site nonlinear oscillator or a nonlinear
Schr\"odinger dimer where one site loses and the other site gains energy at the
same rate. We present a wide class of integrable oscillator type dimers whose
Hamiltonian is of arbitrary even order. Further, we also present a wide class
of integrable and superintegrable nonlinear Schr\"odinger type dimers where
again the Hamiltonian is of arbitrary even order.
