- The familiar picture of magnetic collimation of jets is critiqued. Solutions are derived that explicitly demonstrate the asymptotically parabolic nature of almost all stream lines, more or less consistent with previous discussions. It is then shown that collimation is too slow to be physically relevant when the flow in its uncollimated state is only weakly magnetized. In the alternative and more popular case, where the magnetic field is dynamically significant at all points on the flow, the divergence of field lines to large cylindrical radius implies kink instability. It is shown that the kink instability, for astrophysical parameters, is not expected to stabilize at finite amplitudes, and that magnetically confined jets should therefore be limited to modest collimation in the absence of an additional collimation mechanism. It is conjectured that the kink instability can be mitigated if the jet has inner and outer parts, with only the latter strongly magnetized, as previously proposed by Shu and coworkers for other reasons. The possibility is also considered that magnetic collimation is intrinsically modest.