Eventually found this thread.
A Drexler LSD (lamelle - 40% slip) works just fine (rear diff, front left untouched, ie "open") on my 330i xDrive MY2011. The handling and predictability (especially while hard cornering on icy/slippery roads, DSC off, obviously) improved tenfold. At least.
But, imho LSD (of any kind - I do run a Quaife - a worm type LSD - on the other car of mine, and frankly speaking I would NOT tell Drexler from Quaife, they behave +/- the same) is only half of the fun. Shortening the diff does the second half.
I have both cars shortened quite a lot (3er - 15% both diffs, Z4 - 17% rear one) and the increase in dynamics is overwhelming. Proportionally, the milleage dropped quite a lot, too.