HMP Bristol is "much improved" but high levels of suicide and self-harm among its prisoners remain a concern, say inspectors.
Chief Inspector of Prisons Peter Clarke said the jail was "a more purposeful, safe and decent establishment" than it was at the last inspection in May 2019.
At that time, the prison in Horfield was given the lowest grading possible for safety and purposeful activity.
Mr Clarke said: "At long last" there had been "important changes".
The inspection in 2019 was so troubling it prompted Mr Clarke to invoke a rare "urgent notification" calling on the Secretary of State for Justice to intervene urgently to support the prison.
Mr Clarke had noted "high violence" and "squalid" conditions at the prison, after a decade of "drift and decline".
However, after a scrutiny visit last month the inspector said: "I am pleased to report that we saw enough to be confident that, in our view, Bristol was a much-improved institution."
Despite the overall improvement, Mr Clarke warned that levels of suicide and self-harm must be reduced as a "high priority", according to the BBC's Local Democracy Reporting Service.
"High levels of suicide and self-harm remained a concern, with two self-inflicted deaths in 2020 and one further very recent unexplained death which was under investigation," he said.
"Recorded self-harm incidents were three times higher than at comparator prisons.
"Considerable effort had been made to reduce self-harm, and there were very early indications that these initiatives might be having an impact."
Mr Clarke also made recommendations relating to dental care after finding that prisoners' wait for routine appointments was "as long as six months and increasing".
He also expressed concerns for public protection and said "not all" high-risk prisoners were discussed "in good time" before their release.
HMP Bristol is a category B local and resettlement prison holding about 500 young and adult male prisoners.