  Recent work ([18], [1]) has produced a complete list of weighted homogeneous
surface singularities admitting smoothings whose Milnor fibre has only trivial
rational homology (a "rational homology disk"). Though these special
singularities form an unfamiliar class and are rarely even log-canonical, we
prove the
  Theorem. A rational homology disk smoothing of a weighted homogeneous surface
singularity can always be chosen so that the total space is log-terminal. In
particular, this smoothing is $\Q$-Gorenstein.
  The key idea is to define a finite "graded discrepancy" of a normal graded
domain with $\Q$-Cartier canonical divisor, and to study its behavior for a
smoothing.
