[Contemporary Docs] "The arraignment, tryal, and condemnation of Captain William Kidd"
However, it is worth noting that (like Avery) he heard the siren song of the newly-revealed wealth of the Indian Ocean, which lured him fully into a life of piracy. Kidd had previously stayed within the murky realm of licensed privateers, but when under pressure from his crew to capture a large haul, it was to Madagascar and then the ocean beyond that he set sail.
Kidd's crimes were so notorious, his connections to high-ranking aristocrats so scandalous, and his decision making (in masquerading as a privateer when the practice was waning, and in attempting to conceal his crimes) so poor, that his is a rare case of a very well-documented trial for piracy. Many pirates committed worse crimes than Kidd, but his circumstances meant he was to set an example.
The Library of Congress has digitized the trial, which provides a window into both legal practice and the thorny issues around piracy at the time. You can access it as a PDF here: http://lcweb2.loc.gov/service/lawlib/law0001/2010/201000302205929/201000302205929.pdf