I'm having trouble with contamination of linearized plasmid with the intact circular plasmid. I have heavily overdigested the plasmid, gel purified, and digested with another restriction enzyme, but I still get PCR products over the cut site. This is a problem because I'm trying to do PCR using a bridging oligo which introduces a necessary additional sequence into the cut site, and it seems that there must be no intact plasmid present for this to work.