* Dollar index inches higher 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 (Adds quote, detail, updates prices)
By Neal Armstrong
LONDON, May 3 (Reuters) - The dollar hobbled near a three-year trough against a currency basket on Tuesday, undermined by loose U.S. monetary policy, but analysts said it's fall was looking overextended due to extreme short positioning.
The dollar index, which tracks its performance against a basket of major currencies, was last up 0.3 percent at 73.171, 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 at 0.8619 francs on trading platform EBS in early trade, slipping under Friday's low of 0.8626.
"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 fact currency speculators have already piled up bets against the dollar means the it could get a lift if short-covering sets in.
The euro was down 0.2 percent at $1.4802 after falling back 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.
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 $1.6482 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.
AUSSIE DIPS
The Canadian dollar staged a brief relief rally as Canada's ruling Conservatives won a crushing victory in the federal election.
Provisional results showed the Conservatives had 166 seats in Parliament, well above the 155 they needed to transform their minority government into a majority.
The U.S. dollar was last at C$0.9500, near a 3-1/2 year low of C$0.9440 hit last week.
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 $1.0878, 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 have helped propel the Aussie to a 29-year high of $1.1012 on Monday.
The dollar was down 0.2 percent at 81.02 yen, close to a one-month low of 80.87 hit in late Asian trade. (Additional reporting by Ian Chua, editing by Chris Pizzey)