  If $G$ is a free product of finite groups, let $\Sigma Aut_1(G)$ denote all
(necessarily symmetric) automorphisms of $G$ that do not permute factors in the
free product. We show that a McCullough-Miller [D. McCullough and A. Miller,
{\em Symmetric Automorphisms of Free Products}, Mem. Amer. Math. Soc. 122
(1996), no. 582] and Guti\'{e}rrez-Krsti\'{c} [M. Guti\'{e}rrez and S.
Krsti\'{c}, {\em Normal forms for the group of basis-conjugating automorphisms
of a free group}, International Journal of Algebra and Computation 8 (1998)
631-669] derived (also see Bogley-Krsti\'{c} [W. Bogley and S. Krsti\'{c}, {\em
String groups and other subgroups of $Aut(F_n)$}, preprint] space of pointed
trees is an $\underline{E} \Sigma Aut_1(G)$-space for these groups.
