Relativistic jets in Galactic superluminals and extragalactic active galactic nuclei may be surrounded by a wind near the central engine. Theoretical analysis and numerical simulation reveal considerable stabilization of relativistic jet flow by a wind to helical and higher order asymmetric modes of jet distortion. When velocities are measured in the source (inlet) frame, reduction in the absolute velocity difference between jet and wind, Deltav=v(jet)-v(wnd), provides stabilization in addition to stabilization provided by a high jet Lorentz factor, but a high Lorentz factor wind is not needed to stabilize a high Lorentz factor jet. However, the fundamental pinch mode is not similarly affected, and knots with spacing a few times the jet radius are anticipated to develop in such flows. Thus, we identify a mechanism that can suppress large-scale asymmetric structures while allowing axisymmetric structures to develop. Relativistic jets surrounded by out owing winds will be more stable than if surrounded by a stationary or back owing external medium. Knotty structures along a straight jet like that in 3C 175 could be triggered by pinching of an initially low Mach number jet surrounded by a suitable wind. As the jet enters the radio lobe, suppression of any surrounding out flow or back flow associated with the high-pressure lobe triggers exponential growth of helical twisting.