  In this paper we study the performance in $e^+e^-$ collisions of classical
$e^+e^-$ jet reconstruction algorithms, longitudinally invariant algorithms and
the recently-proposed Valencia algorithm. The study includes a comparison of
perturbative and non-perturbative jet energy corrections and the response under
realistic background conditions. Several algorithms are benchmarked with a
detailed detector simulation at $\sqrt{s}= 3$~\tev. We find that the classical
$e^+e^-$ algorithms, with or without beam jets, have the best response, but are
inadequate in environments with non-negligible background. The Valencia
algorithm and longitudinally invariant $k_t$ algorithms have a much more robust
performance, with a slight advantage for the former.
