  We reexamine the regularization of the two-point function of a scalar field
in a Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. Adiabatic
regularization provides a set of subtraction terms in momentum space that
successfully remove its ultraviolet divergences at coincident points, but can
significantly distort the power spectrum at infrared scales, especially for
light fields. In this work we propose, by using the intrinsic ambiguities of
the renormalization program, a new set of subtraction terms that minimize the
distortions for scales $k \lesssim M$, with $M$ an arbitrary mass scale. Our
method is consistent with local covariance and equivalent to general
regularization methods in curved spacetime. We apply our results to the
regularization of the power spectrum in de Sitter space: while the adiabatic
scheme yields exactly $\Delta_{\phi}^{\rm (reg)} = 0$ for a massless field, our
proposed prescription recovers the standard scale-invariant result
$\Delta_{\phi}^{\rm (reg)} \simeq H^2 /(4\pi^2)$ at super-horizon scales.
