I'm often using the Select by Color or Fuzzy Select tool. ¿Is there a quick way to increment the threshold with a keyboard shortcut, the mouse wheel, or similar?

Take the following example:

Given the image of the GIMP mascot, I want to select only certain portions, for instance the outer white part.

To do this I activate the Select by Color or the Fuzzy Select tool. Set the threshold to a starting value (let's say 15), then click on a white part at the edges of the image. But I'm not quite satisfied with the resulting selection: it selects most of the area I want but not enough of the greyish shadow below the chin. So I adjust the threshold to 50 and click again. Still not enough, set to 90 and lick again. A bit too much, set to 80 and click another. Almost there, set to 85 and click. Set to 83 and finally voilá.

That involved a lot of clicking and typing though. ¿Is there a quicker way to do this? Ideally I would like to see a live update of the selection as I change the threshold, so that I can simply drag the slider or scroll the mouse wheel until it's perfect.

Maybe I'm simply using the wrong tool and there's are completely different inroads to achieve this. I'd like to know about those as well.