  We include new additional absorption corrections into the
Lebiedowicz-Szczurek (non-resonant) model for $p p \to p p \pi^+ \pi^-$ or $p
\bar p \to p \bar p \pi^+ \pi^-$ processes. They are related to the $\pi N$
nonperturbative interaction in the final state of the reaction. The role of the
absorption corrections is quantified for several differential distributions for
$\sqrt{s}$ = 0.2, 1.96, 7, and 8 TeV. The new absorption corrections lead to
further decrease of the cross section by about a factor of two. They change the
shape of some distributions ($d \sigma / dt$, $d \sigma / dp_{t,p}$, $d
\sigma/d \phi_{pp}$) but leave almost unchanged shape of other distributions
($d \sigma / dM_{\pi \pi}$, $d \sigma / dy_{\pi}$, $d \sigma /dp_{t,\pi}$, $d
\sigma/ d \phi_{\pi \pi}$). The effect may have important impact on the
interpretation of the recent STAR and CDF data as well as the forthcoming data
of the ALICE, ATLAS + ALFA and CMS + TOTEM collaborations.
