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Adjective: on the up-and-up
Usage: informal
  1. [N. Amer, informal] Legitimate; honest; upright
     
  2. [Brit, informal] Steadily getting better

Nearest

on the road
on the rocks
on the ropes
on the run
on the side
on the sly
on the spot
on the spur of the moment
on the table
on the trot
on the up-and-up
on the way
on the whole
on the wing
on thin ice
on time
on top of the world
on tour
on trial
on your guard
on/off switch