Answering a question of Rodl and Thoma, we show that the Nibble Algori
thm for finding a collection of disjoint edges covering almost all ver
tices in an almost regular, uniform hypergraph with negligible pair de
grees can be derandomized and parallelized to run in polylog time on p
olynomially many parallel processors. In other words, the nearly-perfe
ct packing problem on this class of hypergraphs is in the complexity c
lass NC.