Transient radio emission from X-ray binaries is associated with synchrotron emission from collimated jets that escape the system, and accreting millisecond X-ray pulsars (AMXPs) are no exception. Although jets from black hole X-ray binaries are well-studied, those from neutron star systems appear much fainter, for reasons yet uncertain. Jets are usually undetectable at higher frequencies because of the relative brightness of other components such as the accretion disc. AMXPs generally have small orbital separations compared with other X-ray binaries and as such their discs are relatively faint. Here, I present data that imply jets in fact dominate the radio-to-optical spectrum of outbursting AMXPs. They therefore may provide the best opportunity to study the behaviour of jets produced by accreting neutron stars, and compare them to those produced by black hole systems.