  Guided by idealized but soluble nonrenormalizable models, a nontraditional
proposal for the quantization of covariant scalar field theories is advanced,
which achieves a term-by-term, divergence-free perturbation analysis of
interacting models expanded about a suitable pseudofree theory (differing from
a free theory by an $\hbar$ term). This procedure not only provides acceptable
solutions for models for which no acceptable solution currently exists, e.g.,
$\phi^4_n$, for spacetime dimension $n\ge4$, but offers a new, divergence-free
solution, for less-singular models as well, e.g., $\phi^4_n$, for $n=2,3$.
