  We construct a list of minimal scale-invariant models at the TeV scale that
generate one-loop neutrino mass and give viable dark matter candidates. The
models generically contain a singlet scalar and a $Z_2$-odd sector comprised of
singlet, doublet and/or triplet SU(2) multiplets. The dark matter may reside in
a single multiplet or arise as an admixture of several multiplets. We find
fifteen independent models, for which the dark matter is a viable candidate and
neutrino mass results from a diagram with just one of the irreducible
scale-invariant one-loop topologies. Further "non-pure" cases give hybrid
one-/two-loop masses. All models predict new TeV scale physics, including a
singlet scalar that generically mixes with the Higgs boson.
