We explore the possibility that extragalactic radio jets might be accelerat
ed by highly disorganized magnetic fields that are strong enough to dominat
e the dynamics until the terminal Lorentz factor is reached. Following the
twin-exhaust model by Blandford & Rees, the collimation under this scenario
is provided by the stratified thermal pressure from an external medium. Th
e acceleration efficiency then depends on the pressure gradient of that med
ium. In order for this mechanism to work there must be continuous tangling
of the magnetic held, changing the magnetic equation of state away from pur
e flux freezing (otherwise, conversion of Poynting flux to kinetic energy f
lux is suppressed). This is a complementary approach to models in which the
plasma is accelerated by large-scale ordered fields. We include a simple p
rescription for magnetic dissipation, which leads to trade-offs among conve
rsion of magnetic energy into bulk kinetic energy, random particle energy,
and radiation. We present analytic dynamical solutions of such jets, assess
the effects of radiation drag, and comment on observational issues, such a
s the predicted polarization and synchrotron brightness. Finally, we try to
make the connection to observed radio galaxies and gamma-ray bursts.