Paste a palette, choose a target color space and click on the button: get a better distribution in the L*a*b* color space. You can set how much correction you want (click on a column).
Restrain the color space if needed:
Hue (range: 0 to 360)
Minimum
Maximum
Chroma (range: 0 to 10)
Minimum
Maximum
Lightness (range: 0 to 10)
Minimum
Maximum