  We define a variant of real-analytic polylogarithms that are single-valued
and that satisfy ''clean'' functional relations that do not involve any
products of lower weight functions. We discuss the basic properties of these
functions and, for depths one and two, we present some explicit formulas and
results. We also give explicit formulas for the single-valued and clean
single-valued version attached to the Nielsen polylogarithms $S_{n,2}(x)$, and
we show how the clean single-valued functions give new evaluations of multiple
polylogarithms at certain algebraic points.
