  A group has finite palindromic width if there exists $n$ such that every
element can be expressed as a product of $n$ or fewer palindromic words. We
show that if $G$ has finite palindromic width with respect to some generating
set, then so does $G \wr \mathbb{Z}^{r}$. We also give a new, self-contained,
proof that finitely generated metabelian groups have finite palindromic width.
Finally, we show that solvable groups satisfying the maximal condition on
normal subgroups (max-n) have finite palindromic width.
