Shortfalls in delivering curriculum and staff training were amongst the weaknesses identified during the January visit.
An improvement plan was imposed at the edge-of-town centre, which had a roll of 255 children, with a follow-up visit taking place last year.
Inspectors found progress had been made during the 2012 follow-up but still demanded better.
And during a visit earlier this year by Education Scotland, the nursery was given a glowing report.
Managing Inspector Barbara Daly said: "Significant changes have been made to the way the playrooms are organised.
"This is resulting in more choices for children and more effective learning environments.
"Children now have an increased choice of activities and this is helping them to sustain concentration and show more commitment to their chosen tasks.
"More real life experiences, for example, planting herbs and baking, are helping children to practice their skills in meaningful contexts."
The thumbs up from inspectors means that no more follow-up visits will take place for the forseeable future.
Ms Daly added: "We have increased confidence in how well the centre improves the quality of its work.
"An appropriate plan is in place for improvement and there is clear evidence of improvements having been made to the quality of the service.
"Managers now have a clearer understanding of the strengths of the nursery and areas where further action is necessary."