  For $\alpha>-1$, let $A^2_{\alpha}$ be the corresponding weighted Bergman
space of the unit ball in $\mathbb{C}^n$. For a bounded measurable function
$f$, let $T_f$ be the Toeplitz operator with symbol $f$ on $A^2_{\alpha}$. This
paper describes all the functions $f$ for which $T_f$ commutes with a given
$T_g$, where $g(z)=z_{1}^{L_1}... z_{n}^{L_n}$ for strictly positive integers
$L_1,..., L_n$, or $g(z)=|z_1|^{s_1}... |z_n|^{s_n}h(|z|)$ for non-negative
real numbers $s_1,..., s_n$ and a bounded measurable function $h$ on $[0,1)$.
