We show that the class {\rm S}_2^p is a subclass of
{{\rm ZPP}^{\rm NP}}. The proof uses universal hashing, approximate counting
and witness sampling. As a consequence, a collapse first noticed by
Samik Sengupta that the assumption NP has small circuits collapses
PH to {\rm S}_2^p
becomes the strongest version to date of the Karp-Lipton Theorem.