  In its simplest form the curvaton paradigm requires the Hubble parameter
during inflation to be bigger than $10^8 \GeV$, but this bound may be evaded in
non-standard settings. In the heavy curvaton scenario the curvaton mass
increases significantly after the end of inflation. We reanalyze the bound in
this set up, taking into account the upper bound on the curvaton mass from
direct decay. We obtain $H_* > 10^8 \GeV$ if the mass increase occurs at the
end of inflation, and $H_* > 10^{-14} \GeV$ if it occurs just before
nucleosynthesis. We then discuss two implementations of the heavy curvaton.
Parameters are constrained in these explicit models, and as a result even
obtaining TeV scale inflation is hard to obtain.
