  In this paper, we study the problem of computing a minimum-width double-strip
or parallelogram annulus that encloses a given set of $n$ points in the plane.
A double-strip is a closed region in the plane whose boundary consists of four
parallel lines and a parallelogram annulus is a closed region between two
edge-parallel parallelograms. We present several first algorithms for these
problems. Among them are $O(n^2)$ and $O(n^3 \log n)$-time algorithms that
compute a minimum-width double-strip and parallelogram annulus, respectively,
when their orientations can be freely chosen.
