The ion-channel laser (ICL) has been proposed as an alternative to the free-electron laser (FEL), replacing the deflection of electrons by the periodic magnetic field of an undulator with the periodic betatron motion in an ion channel. Ion channels can be generated by passing dense energetic electron bunches or intense laser pulses through plasma. The ICL has potential to replace FELs based on magnetic undulators, leading to very compact coherent X-ray sources. In particular, coupling the ICL with a laser plasma wakefield accelerator would reduce the size of a coherent light source by several orders of magnitude. An important difference between FEL and ICL is the wavelength of transverse oscillations: In the former it is fixed by the undulator period, whereas in the latter it depends on the betatron amplitude, which therefore has to be treated as variable. Even so, the resulting equations for the ICL are formally similar to those for the FEL with space charge taken into account, so that the well-developed formalism for the FEL can be applied. The amplitude dependence leads to additional requirements compared to the FEL, e.g. a small spread of betatron amplitudes. We shall address these requirements and the resulting practical considerations for realizing an ICL, and give parameters for operation at UV fundamental wavelength, with harmonics extending into X-rays.