The original Dr. Imposible debuted in Brad Meltzer's Justice League as a villian of unknown origins, but with a similar semblance to Mr. Miracle; the second Dr. Impposible is earth 2 Jimmy Olsen, under a new alias. Both characters share an evident strong connection to the Fourth world.
Original Dr. Impossible
Doctor Impossible was a newcomer on the super-villain scene, and he kept his personal details closely guarded. He wore a dark coloured costume, which is similar in style to that of Mister Miracle, though his heritage as either a New God from Apokolips or New Genesis has yet to be confirmed. Doctor Impossible carries a computerized "Father Box" and teleports via a "hush tube" - both apparently based on Fourth World technologies of the Mother Box and Boom Tube.About a year after the Infinite Crisis, Doctor impossible emerged in the employ of Professor Ivo, gathering parts to be used in the construction of a robot body to house the consciousness of Solomon Grundy.
After stealing Red Tornado's body from the Metal Men and making off with the Parasite's arm, Doctor Impossible lost a fight against Green Lantern, Black Canary and Red Arrow.
Doctor Impossible next appeared with a team he had assembled to help him collect parts of an alien device that made it possible to view the Multiverse. He sent Chair and Tender Mercy to BlackHawk Island to collect one piece whilst Neon Black, Hunter and himself infiltrated the Justice League Satellite to acquire the last part.
With the help of Dr. Sivana, Doctor Impossible built the Methuselah machine for Deathstroke. The machine had the ability to make a man immortal, or raise some one from the dead. The machine was destroyed by Cinder, a member of Deathstroke's team. Doctor Impossible had a chance to save the machine but declined realizing it was an abomination.
Earth 2 Dr. Impossible
A new Dr. Impossible appeared after Flashpoint, but not inthe prime earth. On earth-2, Jimmy Olsen was a prisoner inside Arkham Asylum until he was released by the second Batman (Thomas Wayne), Aquawoman, and other members of the World Army. As a technopath with a photographic memory. He goes by the Super Name of Accountable, which was his web name prior to the events of this series. He got an upgrade later when a Motherbox from Mister Miracle chose to interface with him to help their cause against the forces of Apokolips. Jimmy was pivotal in save two million survivors escape the clutches of Darkseid and his forces. When the survivors reached the New Earth 2 (Telos), Olsen takes the name of Dr. Impossible.