Bubber -- I have a Mk II LH, and it has never been as accurate as I would like. I tried shimming the receiver up with very thin plastic sheeting, to float the barrel -- no change. It shoots about 1.5 to 2" groups at 50 yards from a rest with a scope, no matter which ammo I use. I did the "shim trick" on the trigger and installed an overtravel screw, and the trigger is great now -- breaks at about 2.5 pounds, but that didn't improve the overall accuracy, either.
After all that, I decided to use it for iron-sight shooting, so I lopped off the Monte Carlo comb and fitted a Williams Guide receiver sight and a Shorty ramp and bead, and it gets a lot of use to practice the basics of rifle shooting, sometimes using a sling. I know what it will do with a scope, and I try my best to achieve that with iron sights. I don't often make it, but practicing with an old-fashioned aperture sight does improves my rifle shooting overall.