Renormalization of rational Lagrangians

We show that rational Lagrangians of the type Gφ^ν₀(1 + λφ)^-ν₁ can be renormalized by introducing a finite class of infinite counter terms providing that the Dyson index ν₀ − ν₁ ≤ 3. The form of the counter terms is explicitly exhibited. The theories become unrenormalizable when ν₀ − ν₁ > 3; we discuss, in particular, the case ν₀ − ν₁ = 4, which resembles a gφ⁴ theory for φ → ∞, and is nonrenormalizable, contrary to what one may have naively expected.