  We generalize the Wriggle polynomial, first introduced by L. Folwaczny and L.
Kauffman, to the case of virtual tangles. This generalization naturally arises
when considering the self-crossings of the tangle. We prove that the
generalization (and, by corollary, the original polynomial) are Vassiliev
invariants of order one for virtual knots, and study some simple properties
related to the connected sum of tangles.
