The Cold Dark Matter paradigm successfully explains many phenomena on scales larger than galaxies, but seems to predict galaxy halos which are more centrally concentrated and have a lumpier substructure than observed. Endowing cosmic dark matter with a small primordial velocity dispersion preserves the successful predictions of the Cold Dark Matter scenario on large scales and improves the agreement with halo structure. A “phase density” Q=ρX‹ v 2‹3/2, proportional to the inverse entropy for nonrelativistic matter, is estimated for relativistically decoupled thermal or degenerate relic particles of mass m X : Q=qXgm X 4 , with a numerical factor q x depending on the particle type but no cosmological parameters. Since Q cannot increase for dissipationless, collisionless matter, at a given velocity dispersion there is a maximum space density; this “phase packing” constraint eliminates the singular density predicted by CDM. The core radius r 0 and halo circular velocity v c∞ are related by r 0=0.44(QGvc ∞ )1/3., analogous to the scaling of degenerate dwarf stars. Particle velocities also filter primordial perturbations, with a filtering scale κ X ∝ H 0Ω rel 1/2 (QρX)1/3. Particle candidates for warm matter are briefly discussed; for warm thermal relics to have the observed mass density requires decoupling prior to the QCD epoch and therefore a superweak interaction with thermal Standard Model particles.