The topological disc (De Paepe's)\[P=\{(z^2,\bar{z}^2+\bar{z}^3):|z|\le 1\}\subset {\bb C}^2\]
is shown here to have non-trivial polynomially convex hull. In fact, the authors show that this holds for all discs of the form $X=\{(z^2,f(\bar{z})):|z|\le r\}$, where $f$ is holomorphic on $|z|\le r$, and $f(z)=z^2+a_3z^3+\ldots$, with all coefficients $a_n$ real, and at least one $a_{2n+1}\ne 0$.