  We consider the embedding function $c_b(a)$ describing the problem of
symplectically embedding an ellipsoid $E(1,a)$ into the smallest possible
scaling by $\lambda>1$ of the polydisc $P(1,b)$. In particular, we calculate
rigid-flexible values, i.e. the minimum $a$ such that for $E(1,a')$ with
$a'>a$, the embedding problem is determined only by volume. For $1<b<2$ we find
that these values vary piecewise smoothly outside a discrete set of
discontinuities at $b\in\left(\frac{n+1}{n}\right)^2$.
