Consideration of the analytic properties of pion-induced baryon self-energi
es leads to new functional forms for the extrapolation of light baryon mass
es. These functional forms reproduce the leading non-analytic behavior of c
hiral perturbation theory, the correct non-analytic behavior at the N pi th
reshold and the appropriate heavy-quark limit. They involve only three unkn
own parameters, which may be obtained by fitting to lattice data. Recent dy
namical fermion results from CP-PACS and UKQCD are extrapolated using these
new functional forms. We also use these functions to probe the limit of ap
plicability of chiral perturbation theory to the extrapolation of lattice Q
CD results.