Directional control after touchdown...

I've got a question for the group. Suppose you find yourself in the
following situation:

You are flying a C182, landing on runway 22. The ATIS lists the winds
as 240 at 10. The windsock is not visible.

You approach at a normal airspeed, full flaps, coming over the numbers
at 65 kts. The mains touchdown, followed by the nosegear. Slight
right aileron is being maintained into the wind. Everything is
aligned properly and on the centerline at touchdown.

After touchdown the plane starts to drift to the right side of the
runway. You try to correct by pointing the nose back to the
centerline with left rudder. The nose seems to be pointed left, but
the plane is still drifting right. It feels like any more left rudder
could result in bad skidding and/or a ground loop.

What are the proper control inputs to correct the situation?

Left aileron would be in the _opposite_ direction of the indicated
crosswind. Increasing back pressure would make the nosewheel even
less effective.

--Dan