  By the famous ADE classification rational double points are simple. Rational
triple points are also simple. We conjecture that the simple normal surface
singularities are exactly those rational singularities, whose resolution graph
can be obtained from the graph of a rational double point or rational triple
point by making (some) vertex weights more negative. For rational singularities
we show one direction in general, and the other direction (simpleness) within
the special classes of rational quadruple points and of sandwiched
singularities.
