* Dollar index up 0.5 pct on day but in sight of 3-yr lows
* Short positions in greenback start to look overdone
* Sterling slumps as weak data pushes back rate hike chances
(Recasts, adds detail, updates prices)
By Neal Armstrong
LONDON, May 3 (Reuters) - The dollar edged off three-year lows on Tuesday as a build-up of bets to sell it based on loose U.S monetary policy ran out of steam, though gains against the euro were capped by good demand on dips for the shared currency.
The dollar index, which tracks its performance against a basket of major currencies, was last up 0.5 percent at 73.296, still not far off a three-year low of 72.722 hit this week. Its decline in the past few weeks has taken it ever closer to a record low of 70.698 set in March 2008.
The dollar slipped to a record low against the Swiss franc around 0.8615 francs, slipping under Friday's low of 0.8626.
The fact currency speculators have already piled up bets against the dollar means it could get a lift if short-covering sets in.
"In the near term the dollar's fall could extend further still but levels are now becoming more stretched in terms of valuation and positioning. Momentum indicators are also showing the dollar is very oversold," said Lee Hardman, currency strategist at BTM-UFJ.
The euro was down 0.4 percent at $1.4772 after falling to $1.4751 in early European trade. Dealers reported good demand to buy into the $1.4750 zone.
"It's very much a case of buying the dips in euro/dollar at these levels. Rate hike expectations are anchoring the euro," said Chris Walker, currency strategist at UBS in London.
The single currency hit a 17-month high of $1.4903 on Monday on trading platform EBS on the view that euro zone interest rate would be raised again this year, in contrast to an ultra-loose outlook for U.S. monetary policy.
Surging energy costs drove euro zone producer price inflation to its highest level in 2-1/2 years in March, strengthening the case for more interest rate rises.
STERLING KNOCKED
Sterling fell to its lowest level since March 2010 against the euro at 89.80 pence after a survey of UK manufacturing came in below market expectations. The pound also shed over half a U.S. cent to trade at $1.6468 against the dollar.
"Core UK data has begun to disappoint to the downside. It seems like all bets are off for a UK rate hike until year-end," said Walker at UBS.
The Canadian dollar pared gains after a brief relief rally as Canada's ruling Conservatives won a crushing victory in the federal election.
The U.S. dollar was last at C$0.9538, up around 0.4 percent on the day after slipping to C$0.9460 in overnight trade.
The Australian dollar dipped after Australia's central bank kept interest rates unchanged at 4.75 percent as expected. The Reserve Bank of Australia said underlying inflation looked to have bottomed and would increase somewhat as the economy strengthened, sounding a little less hawkish than some analysts had expected.
The Aussie dollar last stood at $1.0859, having dipped from around $1.0920 after the RBA's decision.
Sentiment for the U.S. dollar has been overwhelmingly bearish as ultra-loose U.S. monetary policy has made it the funding currency of choice in popular carry trades that helped propel the Aussie to a 29-year high of $1.1012 on Monday.
The dollar hit a one-month low around 80.79 yen in late morning trade, with the yen helped by a broad fall in global equity markets.
(Editing by Chris Pizzey/Ruth Pitchford)