  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.
