Primordial spectral indices are calculated to second order in slow-roll parameters for three closely-related models of inflation, all of which contain a scalar field non-minimally coupled to the Ricci curvature scalar. In most cases, $n_s$ may be written as a function of the non-minimal curvature coupling strength $ξ$ alone, with $n_s (ξ) \leq 1$, although the constraints on $ξ$ differ greatly between \lq new inflation' and \lq chaotic inflation' initial conditions. Under \lq new inflation' initial conditions, there are discrepancies between the values of $n_s$ as calculated in the Einstein frame and the Jordan frame. The sources for these discrepancies are addressed, and shown to have negligible effects on the numerical predictions for $n_s$. No such discrepancies affect the calculations under \lq chaotic inflation' initial conditions.

31 pp. Forthcoming in Physical Review D. Section 3 significantly revised. Four figures not included; hard copies available from author