As Henry was a usurper, it was unlikely that he'd gained much support and loyalty from his Nobles although it did not evade the fact that he had to establish some authority over them. One of the primary methods Henry used was to either punish or reward his Nobility with his financial policies.
Henry had a very detailed and complex financial policy which enabled him to milk every penny he could from his Nobility or in fact avoid having to pay them all together. A prime example would be Henry's reluctance to grant titles and land as rewards, instead he preferred to award the ancient honour of the Order of the Garter. This significantly decreased the amount Henry had to pay out to his Nobles but it also kept them satisfied as it was such a prestigious award. Henry also used Bonds and Recognisances to restrain the power of his Nobility. Lord Burgavenny, for example, was fined £70,650 for the breach of such a Recognisance. This obviously contain the power of over mighty Nobles as it was estimated that between the years 1504-1508, Edmund Dudley collected £50,000 per annum from bonds. Such methods aided with controlling Nobility but there were other financial policies that contributed.
Every monarch of the time had to handle their Nobility, and it was no different for Henry. In fact Henry used very effective policies in order to strengthen his control over them. A notable policy would be the Acts of Attainders, in 1485 & 1504 he used this policy to declare 56 Nobleman guilty of crimes against the Crown. Thomas Howard lost the title Duke of Norfolk and his family estates after Bosworth, Henry was able to gain huge amounts of income from these Acts which increased his fragile control over the Nobility. As a result of the Acts of Attainders, the about of over mighty noble families numbered 5 in 1497, this shows how successful his financial