  We show that any $y$-monotone poly-line drawing can be straightened out while
maintaining $y$-coordinates and height. The width may increase much, but we
also show that on some graphs exponential width is required if we do not want
to increase the height. Likewise $y$-monotonicity is required: there are
poly-line drawings (not $y$-monotone) that cannot be straightened out while
maintaining the height. We give some applications of our result.
