The double guillotine has two blades set in a frame with a hole for the cigar head to fit in.  This cutter has the advantage of approaching the cap from two sides, which can minimize the risk of tearing the wrapper.  A sharp blade, a quality frame, and solid technique, are still necessary to produce The Perfect Cut.  Contrary to popular belief, double guillotines are not self-sharpening, but they will stay sharp longer, since each blade is doing half the work.