  The incorporation of a small cosmological constant within radiatively-broken
scale-invariant models is discussed. We show that phenomenologically consistent
scale-invariant models can be constructed which allow a small positive
cosmological constant, providing certain relation between the particle masses
is satisfied. As a result, the mass of the dilaton is generated at two-loop
level. Another interesting consequence is that the electroweak
symmetry-breaking vacuum in such models is necessarily a metastable `false'
vacuum which, fortunately, is not expected to decay on cosmological time
scales.
