  Let $M$ be a tame mouse modelling ZFC. We show that $M$ satisfies ``there is
a real $x$ such that every set is OD in $x$'', and that the restriction of the
extender sequence of $M$ to the interval $[\omega_1^M,\infty)$ is definable
without parameters over the universe of $M$. We show that $M$ has universe
$H[X]$, where $H=\mathrm{HOD}^M$ and $X=M|\omega_1^M$ is the initial segment of
$M$ of height $\omega_1^M$ (including the restriction of $M$'s extender
sequence through $\omega_1^M$), and that $H$ is the universe of a premouse over
some $t\subseteq\omega_2^M$. We also show that $M$ has no proper grounds via
strategically $\sigma$-closed forcings.
  We then extend some of these results partially to non-tame mice, including a
proof that many natural $\varphi$-minimal mice model ``$V=\mathrm{HOD}$'',
assuming a certain fine structural hypothesis whose proof has almost been given
elsewhere.
