  Motivated by the string landscape we examine scenarios for which inflation is
a two-step process, with a comparatively short inflationary epoch near the
string scale and a longer period at a much lower energy (like the TeV scale).
We quantify the number of $e$-foldings of inflation which are required to yield
successful inflation within this picture. The constraints are very sensitive to
the equation of state during the epoch between the two inflationary periods, as
the extra-horizon modes can come back inside the horizon and become
reprocessed. We find that the number of $e$-foldings during the first
inflationary epoch can be as small as 12, but only if the inter-inflationary
period is dominated by a network of cosmic strings (such as might be produced
if the initial inflationary period is due to the brane-antibrane mechanism). In
this case a further 20 $e$-foldings of inflation would be required at lower
energies to solve the late universe's flatness and horizon problems.
