  In this brief note, we investigate the $\mathbb{CP}^2$-genus of knots, i.e.
the least genus of a smooth, compact, orientable surface in
$\mathbb{CP}^2\setminus \mathring{B^4}$ bounded by a knot in $S^3$. We show
that this quantity is unbounded, unlike its topological counterpart. We also
investigate the $\mathbb{CP}^2$-genus of torus knots. We apply these results to
improve the minimal genus bound for some homology classes in $\mathbb{CP}^2\#
\mathbb{CP}^2$.
