  Hyperbolic monopole solutions can be obtained from circle-invariant ADHM data
if the curvature of hyperbolic space is suitably tuned. Here we give explicit
ADHM data corresponding to axial hyperbolic monopoles in a simple, tractable
form, as well as expressions for the axial monopole fields. The data is
deformed into new 1-parameter families preserving dihedral and twisted-line
symmetries. In many cases explicit expressions are presented for their spectral
curves and rational maps of both Donaldson and Jarvis type.
