"A somewhat more difficult question. 'Sir' is a safe bet. 'Gregor' if and only if invited. Avoid 'sire' at least at first - it's reserved for Barrayaran Imperial subjects, of which you can technically be said to be one, but it denotes an oath relationship and you haven't taken any. Avoid Your Adjectiveness-type addresses, too - Barrayar doesn't use 'em. See, Barrayaran formal address for Gregor is 'sire' the way Barrayaran formal address for one's own Count or his heir is 'my lord', but we spent six hundred years having lots of Counts and only one Emperor - there was never a reason to have a tradition for how to talk to the Emperor when you're not his subject. And we've only had eighty years to deal with the new situation, so nothing's really stuck yet. You can also get away with addressing him as appropriate for Count Vorbarra, which he also is, if you see him in his House uniform - black and silver as opposed to the Imperial red and blue. 'Emperor Gregor' by analogy to Lord or Count Firstname has sort of been tried now and then and hasn't caught on hugely, but it's technically acceptable if you get tired of sir-ing him all the time but still aren't on friendly terms."