  The rise in the cosmic-ray positron fraction measured by the PAMELA satellite
is likely due to the presence of astrophysical sources of positrons, e.g.
pulsars, on the kpc scale around the Earth. Nevertheless, assessing the
properties of these sources from the positron data requires a good knowledge of
the secondary positron component generated by the interaction of cosmic rays
with the interstellar gas. In this paper, we investigate the impact of the
spectral hardening in the cosmic-ray proton and helium fluxes recently reported
by the ATIC2 and CREAM balloon experiments, on the predictions of the secondary
positron flux. We show that the effect is not negligible, leading to an
increase of the secondary positron flux by up to $\sim$60% above $\sim$100 GeV.
We provide fitting formulae that allow a straightforward utilization of our
results, which can help in deriving constraints on one's favorite primary
positron source, e.g. pulsars or dark matter.
