A hopf algebra of weak compositions WCQSYM is defined, using power series with exponent being not necessarily the natural numbers, certain semi groups. Despite living in an uncommon space, the ordinary QSYM is actually a quotient of WCQSYM. More interestingly, there is a way of seeing WCQSYM as the free object on one generator in the (unheard of before, to me) category of Rota-Baxter algebras.