  We study Kauffman's model of folded ribbon knots: knots made of a thin strip
of paper folded flat in the plane. The folded ribbonlength is the length to
width ratio of such a ribbon knot. We give upper bounds on the folded
ribbonlength of 2-bridge, $(2,q)$ torus, twist, and pretzel knots, and these
upper bounds turn out to be linear in the crossing number. We give a new way to
fold $(p,q)$ torus knots and show that their folded ribbonlength is bounded
above by $2p$. This means, for example, that the trefoil knot can be
constructed with a folded ribbonlength of 6. We then show that any $(p,q)$
torus knot $K$ with $p\geq q>2$ has a constant $c>0$, such that the folded
ribbonlength is bounded above by $c\cdot Cr(K)^{1/2}$. This provides an example
of an upper bound on folded ribbonlength that is sub-linear in crossing number.
