  We study the closure of the cubic Principal Hyperbolic Domain and its
intersection $\mathcal{P}_\lambda$ with the slice $\mathcal{F}_\lambda$ of the
space of all cubic polynomials with fixed point $0$ defined by the multiplier
$\lambda$ at $0$. We show that any bounded domain $\mathcal{W}$ of
$\mathcal{F}_\lambda\setminus\mathcal{P}_\lambda$ consists of $J$-stable
polynomials $f$ with connected Julia sets $J(f)$ and is either of \emph{Siegel
capture} type (then $f\in \mathcal{W}$ has an invariant Siegel domain $U$
around $0$ and another Fatou domain $V$ such that $f|_V$ is two-to-one and
$f^k(V)=U$ for some $k>0$) or of \emph{queer} type (then at least one critical
point of $f\in \mathcal{W}$ belongs to $J(f)$, the set $J(f)$ has positive
Lebesgue measure, and carries an invariant line field).
