  We consider Toeplitz operators with bounded symbol acting on the Bergman
space of the unit disk and assess their hyponormality. We will mainly be
concerned with the symbol $\varphi(z)=z^{n}|z|^{2s}+a(t)\bar{z}^{m}|z|^{2t}$,
where $s$ and $t$ are positive real numbers and $m$ and $n$ are natural
numbers. The main goal is to understand how large $|a(t)|$ can be for this
operator to be hyponormal and we will answer this question for large values of
$t$. We also correct a typo from a 2019 paper of Fleeman and Liaw concerning
the norm of the commutator of the Toeplitz operator with symbol $z^m\bar{z}^n$
when $m>n$.
