* Euro near recent peaks on higher short term rates
* 3-mth eurodollar cross currency swaps show euro premium
* Bullard talks about possibility of small taper in Dec
LONDON, Dec 10 (Reuters) - The euro rose to a six-week peak against the dollar on Tuesday and hovered just below a five-year peak versus the yen, helped by higher short-term market rates and the European Central Bank's reluctance to ease policy again.
Tighter money market conditions in the euro zone, as reflected in the rise of two-year swap rates partly due to year-end factors and the ECB's unwillingness to ease monetary policy soon to fight disinflation, are seeing rate differentials more in favour of the euro.
Against the dollar, the euro was slightly higher at $1.3745 , not far from a two-year high of $1.3833 set in late October. The euro hit a five-year peak of 142.19 yen, a high not seen since October 2008.
The euro has gained over 1.5 percent against the dollar and 2.7 percent versus the yen since the ECB last week refrained from following up on November's rate cut and said it has yet to come up with a detailed plan of which tools to use and when.
"It is a combination of lack of urgency on the part of the ECB and the tighter liquidity conditions that are driving the euro higher," said Alvin Tan, currency strategist at Societe Generale. "The year's high of $1.3833 is definitely in play and we could expect it to go even higher."
Liquidity conditions in the euro zone money market usually tighten towards the end of the year as banks refrain from lending to each other. This year another factor driving euro strength is European banks repatriating funds to shore up their capital bases ahead of an ECB asset quality review.
The review will be based on banks' balance sheets at the end of 2013.
Highlighting this demand, three-month eurodollar cross currency basis swaps moved into positive territory for the first time since 2008. In other words, euro zone banks are paying a premium to buy euros in exchange for dollars.
"Unless the ECB identifies a way and announces a method to counter these tight liquidity conditions, euro/dollar could be dragged as high as $1.39 by year-end," said Chris Turner, head of currency strategy at ING.
In a speech on Tuesday, ECB President Mario Draghi gave no hints that the bank was preparing to take any fresh measures to loosen conditions.
The euro's rise saw the dollar index extend losses into a second straight day. It stayed near six-week lows, dragged down by lower U.S. Treasury yields.
Traders said investors seemed to have pretty much priced in the risk of the Federal Reserve scaling back monetary policy soon, which might help explain why the dollar has not risen broadly in the past few sessions.
Economists polled by Reuters on Monday expect the Fed will begin reducing its massive bond-buying programme in March, but some are warming up to the idea of a December or January taper.
James Bullard, the St. Louis Fed president, said the Fed could slightly reduce its monthly bond purchases this month in reaction to signs of an improved labour market. The Fed holds its policy meeting next week.
Against the yen, though, the greenback held at 103.10 yen not far from a five-year peak of 103.74 set in May.
One possible concern for yen bears is support for Japanese Prime Minister Shinzo Abe dropped after he steamrolled through parliament a tough secrecy act that critics fear could muzzle media and allow officials to hide misdeeds.