  We treat the ultraviolet problem for polaron-type models in nonrelativistic
quantum field theory. Assuming that the dispersion relations of particles and
the field have the same growth at infinity, we cover all subcritical
(superrenormalisable) interactions. The Hamiltonian without cutoff is exhibited
as an explicit self-adjoint operator obtained by a finite iteration procedure.
The cutoff Hamiltonians converge to this operator in the strong resolvent sense
after subtraction of a perturbative approximation for the ground-state energy.
