  We study the Selmer variety associated to a canonical quotient of the
$\Q_p$-pro-unipotent fundamental group of a smooth projective curve of genus at
least two defined over $\Q$ whose Jacobian decomposes into a product of abelian
varieties with complex multiplication. Elementary multi-variable Iwasawa theory
is used to prove dimension bounds, which, in turn, lead to a new proof of
Diophantine finiteness over $\Q$ for such curves.
