Improved cylinder is another of those terms that has different definitions depending which side of the Atlantic you're on. What the Brits call IC, we call skeet. Basically around .005 in a 12ga. What we call IC, they call quarter choke. The French seem to agree with the Brits--which certainly isn't always the case. I recently bought a 12ga Vouzelaud which their description lists as "lisse ameliore" (IC) in the R barrel, "1/4 choke" in the L. Measures 005/011.
I like skeet (or Brit IC) in the R barrel for most of the upland hunting I do. (Even more open doesn't hurt for ruffed grouse and woodcock.) Some think it on the light side for pheasants, but I've found it quite effective, pushing a 1 1/16 oz load of Brit 6's. Light mod makes a good L barrel choice I think, hunting over good dogs. But American IC splits the difference between the two quite nicely, and can be effective out to 40 yards with the right load.