  We study the properties of Fermi Liquids with the microscopic constraint of a
local self-energy. In this case the forward scattering sum-rule imposes strong
limitations on the Fermi-Liquid parameters, which rule out any Pomeranchek
instabilities. For both attractive and repulsive interactions, ferromagnetism
and phase separation are suppressed. Superconductivity is possible in an s-wave
channel only. We also study the approach to the metal-insulator transition, and
find a Wilson ratio approaching 2. This ratio and other properties of
Sr_{1-x}La_xTiO_3 are all consistent with the local Fermi Liquid scenario.
