Conrad had to enforce his royal prerogatives in the Duchy of Carinthia and the Duchy of Swabia. Duke Adalbero of Carinthia had been appointed as duke in 1012 under Emperor Henry II and remained loyal to imperial authority, supporting Conrad's election as German king in 1024. At a synod in Frankfurt in September 1027, Conrad attempted to resolve the decades' long "Gandersheim Conflict". Adalbero accompanied the Emperor and acted as his sword-bearer during the proceeding, indicating Conrad's trust in him. From 1028 on, Adalbero governed his Duchy as an independent state.