  We study Kauffman's model of folded ribbon knots: knots made of a thin strip
of paper folded flat in the plane. The ribbonlength is the length to width
ratio of such a folded ribbon knot. We show for any knot or link type that
there exist constants $c_1, c_2>0$ such that the ribbonlength is bounded above
by $c_1\cdot Cr(K)^2$, and also by $c_2\cdot Cr(K)^{3/2}$. We use a different
method for each bound. The constant $c_1$ is quite small in comparison to
$c_2$, and the first bound is lower than the second for knots and links with
$Cr(K)\leq$ 12,748.
