  We introduce a new knot diagram invariant called the Self-Crossing Index
(SCI). Using SCI, we provide bounds for unknotting two families of framed
unknots. For one of these families, unknotting using framed Reidemeister moves
is significantly harder than unknotting using regular Reidemeister moves.
  We also investigate the relation between SCI and Arnold's curve invariant St,
as well as the relation with Hass and Nowik's invariant, which generalizes
cowrithe. In particular, the change of SCI under {\Omega}3 moves depends only
on the forward/backward character of the move, similar to how the change of St
or cowrithe depends only on the positive/negative quality of the move.
