  In a weakly coupled ultrarelativistic plasma, $1 + n \leftrightarrow 2 + n$
scatterings, with $n \ge 0$, need sometimes to be summed to all orders, in
order to determine a leading-order interaction rate. To implement this "LPM
resummation", kinematic approximations are invoked. However, in cosmological
settings, where the temperature changes by many orders of magnitude and both
small and large momenta may play a role, such approximations are not always
justified. We suggest a procedure to smoothly interpolate between LPM-resummed
$1 + n \leftrightarrow 2 + n$ and Born-level $1 \leftrightarrow 2$ results,
rendering the outcome applicable to a broader range of masses and momenta. The
procedure is illustrated for right-handed neutrino production from a Standard
Model plasma, and dilepton production from a QCD plasma.
