  We study several problems on geometric packing and covering with movement.
Given a family $\mathcal{I}$ of $n$ intervals of $\kappa$ distinct lengths, and
another interval $B$, can we pack the intervals in $\mathcal{I}$ inside $B$
(respectively, cover $B$ by the intervals in $\mathcal{I}$) by moving $\tau$
intervals and keeping the other $\sigma = n - \tau$ intervals unmoved? We show
that both packing and covering are W[1]-hard with any one of $\kappa$, $\tau$,
and $\sigma$ as single parameter, but are FPT with combined parameters $\kappa$
and $\tau$. We also obtain improved polynomial-time algorithms for packing and
covering, including an $O(n\log^2 n)$ time algorithm for covering, when all
intervals in $\mathcal{I}$ have the same length.
