Instead of using the old mini blind slats, hand sew small plastic rings to the places where the slats above have their holes. Thread the mini-blind string through the rings and tie at the bottom ring. OR glue/sew pockets using add'l liner fabric to hide slats. See PureOfFaith.blogspot.com in favorites.
DIY Roman Shade Fashion an easy window treatment by pairing a finished rectangle of fabric with two sets of contrasting ties. Gather the fabric to the desired length and knot the ties, then hang the fabric from a tension rod.