(Adds strategist quote and details throughout; updates prices) * Canadian dollar strengthens 0.3% against the greenback * Price of U.S. oil settles 1.6% higher * Canadian building permits fall by 0.5% in April * Canadian bond yields were little changed across the curve By Fergal Smith TORONTO, June 2 (Reuters) - The Canadian rose against its broadly stronger U.S. counterpart on Wednesday as oil prices climbed and a key level of technical support held up, with the currency moving back toward a six-year high it notched the day before. The loonie was trading 0.3% higher at 1.2037 to the greenback, or 83.08 U.S. cents. On Tuesday, it touched its strongest level since May 2015 at 1.2007. The ability of the currency to stay at levels stronger than 1.2080 despite widespread gains for the greenback overnight has "helped give Canadian dollar buyers some confidence today," said Erik Bregar, head of FX strategy at the Exchange Bank of Canada. The loonie hasn"t closed at a level weaker than 1.2080 since last Wednesday. Oil, one of Canada"s major exports, was supported by an OPEC+ decision to stick to its plan to restore supply to the market gradually and by the slow pace of nuclear talks between Iran and the United States. U.S. crude oil futures settled 1.6% higher at $68.83 a barrel. The U.S. dollar edged up, backing off of a near five-month trough versus major peers, as traders waited for employment data later in the week before making any big moves. Canada"s jobs report for May is due on Friday which could help provide clues on the Bank of Canada"s policy outlook. The central bank will taper its asset purchase programme again next quarter and raise interest rates earlier than previously predicted amid expectations for a robust economic recovery after a recent downturn, a Reuters poll showed. The value of Canadian building permits fell by less than expected in April, dropping 0.5%, after a record increase in March, Statistics Canada data showed. Canadian government bond yields were little changed across the curve, with the 10-year up half a basis point at 1.497%. (Reporting by Fergal Smith Editing by David Holmes and Nick Zieminski) Our Standards: The Thomson Reuters Trust Principles.