Corkscrew

I'm trying to model a corkscrew but am having some trouble. I can get
the main part of it with a helix sweep but that's about it (and it's
not much). I need to extend one end of screw into a straight piece
(somehow add a profile onto the helix). I'm thinking a 3d sketch for
that but not really sure the correct way.

The other portion I'm having problems with is the end that should
taper to a point (the part that pierces a cork). Here my thinking is
to extend the helix some more and create a small circle on one end and
use the end of the screw on the other end and loft together with the
new helix as a guide curve.

I've looked on 3d content to find something similar but can't. I've
found a few around the web but all are in eDrawings and I can't see
the features used to build.

Anyone modeled one before that I could take a look at the feature
steps, or describe it.

Thanks