Adigeon Prime's legal system afforded a great deal of privacy guarantees to those who lived and did business there. As such, this made it very difficult for outside law enforcers to gather evidence of criminal activities on the planet.
In 2155, after Charles "Trip" Tucker had faked his death aboard the starship Enterprise, he was transported to Adigeon Prime, where he underwent cosmetic and genetic surgery to appear as a Romulan. (ENT novel: The Good That Men Do)
In 2348, Richard and Amsha Bashir brought their son Julian to Adigeon Prime to undergo illegal genetic enhancement. Bashir experienced flashbacks to his time on Adigeon Prime in 2376 during his contact with an artifact in the Gamma Quadrant. (DS9 episode: "Doctor Bashir, I Presume"; DS9 - Mission: Gamma novel: Cathedral)