  We construct an optimally local perfect lattice action for free scalars of
arbitrary mass, and truncate its couplings to a unit hypercube. Spectral and
thermodynamic properties of this ``hypercube scalar'' are drastically improved
compared to the standard action. We also discuss new variants of perfect
actions, using anisotropic or triangular lattices, or applying new types of
RGTs. Finally we add a \lambda \phi^4 term and address perfect lattice
perturbation theory. We report on a lattice action for the anharmonic
oscillator, which is perfect to O(\lambda).
