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?