underline-minimum-offset

underline-minimum-offset is a variable defined in `C source code'.
Its value is

1

Documentation:
Minimum distance between baseline and underline.
This can improve legibility of underlined text at small font sizes,
particularly when using variable `x-use-underline-position-properties'
with fonts that specify an UNDERLINE_POSITION relatively close to the
baseline. The default value is 1.

You can customize this variable.

This variable was introduced, or its default value was changed, in version 23.1 of Emacs.