Brooke Mueller -- A Free Woman Again!

Brooke Mueller clearly impressed the prosecutor and judge in her cocaine possession case, because they have terminated her probation months before it was scheduled to end ... TMZ has learned.

Sources tell us ... Brooke's lawyer, Yale Galanter, met with prosecutor Arnie Mordkin in Aspen, Mordkin agreed to end Brooke's supervised probation and on January 3, the judge made it official.

We're told the prosecutor and judge felt Brooke had obeyed all laws -- which she was required to do -- and was conducting herself in a responsible manner. Short story -- they felt Brooke was being so responsible, they cut her a break.

Assuming Brooke stays on the straight and narrow ... the case will be erased from her record in May.

Good to see she's doing well.