Malcolm took advantage of the fact that the English were preoccupied with Danish raids and marched south, winning the Battle of Carham against the Angles in 1018 and thereby regaining Lothian. Thirteen years later King Canute invaded Scotland and forced Malcolm to submit to him. However, Canute seems to have recognized Malcolm's possession of Lothian.
After Malcolm II's reign, Scottish succession was based on the principle of direct descent. Previously, succession was determined by tanistry - during a king's lifetime an heir was chosen and known as "tanaiste rig" (second to the king).