  We consider the issue of selecting parameters and their associated ranges for
carrying out searches for continuous gravitational waves from steadily rotating
neutron stars. We consider three different cases (i) the "classic" case of a
star spinning about a principal axis; (ii) a biaxial star, not spinning about a
principal axis; (iii) a triaxial star spinning steady, but not about a
principal axis (as described in Jones, MNRAS vol 402, 2503 (2010)). The first
of these emits only at one frequency; the other two at a pair of harmonically
related frequencies. We show that in all three cases, when written in terms of
the original "source parameters", there exist a number of discrete
degeneracies, with different parameter values giving rise to the same
gravitational wave signal. We show how these can be removed by suitably
restricting the source parameter ranges. In the case of the model as written
down by Jones, there is also a continuous degeneracy. We show how to remove
this through a suitable rewriting in terms of "waveform parameters", chosen so
as to make the specialisations to the other stellar models particularly simple.
We briefly consider the (non-trivial) relation between the assignment of prior
probabilities on one set of parameters verses the other. The results of this
paper will be of use when designing strategies for carrying out searches for
such multi-harmonic gravitational wave signals, and when performing parameter
estimation in the event of a detection.
