You are getting those extra lines because you are using a LINE_STRIP.
In your 'F' case, push both end points of your line into the vector (like you were doing originally).
_vertexVector.push_back(_prevState.position);
_vertexVector.push_back(_currState.position);
And when you draw, use LINE_LIST instead.
Corey Ross
2009-06-22 00:22:46