Henry dated the start of his reign from the day beforeBosworth - meant those who fought him were traitors and he could have their estatesseized, adding to the king's wealth
Henry arranged for his coronation for 30 October 1485 which was beforeparliamentmet, meaning it could not be claimed that he was kingonly because of parliament
Henry asked for a papal dispensation to allow him to marry Elizabeth of York, distant cousin, to unite the houses of Lancaster and York
He marriedElizabeth after he was crowned, so it could not be claimed that he owed the crown to his wife
When Henry won at Bosworth, he was largely unknown in England, having spent 14years in exile in France after 1471
Likely that many thought that, given his weak claim and lack of knowledge about the country, that his reign would be unlikely to last
Advantages:
Country was weary of war and would support a king who could offer peace and stability
Henry was replacing an unpopular king
Henry wasn't dependent on a powerful noble to make him King so wasn't indebted to one