Reduce the minimum iPhone volume (bluetooth speakers)

When connecting my iPhone (4S or 6) to a JBL Flip 2 bluetooth speakers, the minimum volume is too loud. Under that, it mutes. It is not a problem of the speakers, as the volume using another, non-Apple, phone, can be reduced much more.

Is there a way to get finer decrements of the volume than those of the side buttons? Moving the slider suggests so, but it is difficult to control in such small space.

I tried using a volume cap as suggested elsewehere, but there seems to have no effect on the volume precision.

Any ideas?

I was just here searching for a way to do exactly this (reduce the "Step" for volume adjustments). I gave up and went to solve a couple more music/iPhone related problems.

Anyway, turns out that if you have the Apple Watch and use it's built-in volume control, there are no stops--even when playing through bluetooth it let me adjust all the way from really loud down to whisper.

Another thing to notice--after I adjust my phone volume with the watch I think it somehow affects the built-in controls and I'm able to get a different range but I can't put my finger on exactly what's going on--and after I leave it sit for a while it goes back to it's old behavior.