The LH and KL services are operated by PrivatAir. In addition PrivatAir operate the ZRH EWR service for LX.
PrivatAir operate up to 60 Atlantic crossings a week on A319LR/B737IGW equipment, including the world's highest utilisation B737 between AMS and IAH which is in the air 21 hours out of 24 - 6,700 hours in 2006.
All current scheduled operations involve crew layovers. Nice lifestyle with 4 flights per month for the crews, many of whom came from short haul where they operated that many sectors every two days before.