  Recent observations of M87 and some blazars reveal violent activity in small
regions located at relatively large distances from the central engine.
Motivated by these considerations, we study the hydrodynamic collimation of a
relativistic cooling outflow using a semi-analytical model developed earlier.
We first demonstrate that radiative cooling of the shocked outflow layer can
lead to a focusing of the outflow and its reconfinement in a region having a
very small cross-sectional radius. Such a configuration can produce rapid
variability at large distances from the central engine via reflections of the
converging recollimation shock. Possible applications of this model to TeV
blazars are discussed. We then apply our model to M87. The low radiative
efficiency of the M87 jet renders focusing unlikely. However, the shallow
profile of the ambient medium pressure inferred from observations, results in
extremely good collimation that can explain the reported variability of the
X-ray flux emitted from the HST-1 knot.
