* Euro/yen pulls away from previous day's 18-month high
* Yen takes breather after recent slide
* Dollar/yen pauses after hitting 29-month peak
SINGAPORE, Jan 3 (Reuters) - The yen edged higher after hitting a 29-month low versus the dollar on Thursday, having come under pressure earlier when U.S. lawmakers forged a deal to avoid a fiscal crunch, fuelling demand for riskier investments.
The dollar slipped 0.1 percent to 87.21 yen. The dollar rose to as high as 87.36 yen earlier on Thursday on trading platform EBS, the greenback's highest level against the Japanese currency since late July 2010.
"Technically dollar/yen looks somewhat overbought here. It's gone a long way in a very short time," said Callum Henderson, global head of FX research for Standard Chartered Bank in Singapore, adding that the dollar could see some consolidation in the near term before heading higher.
"Over the next few months, I think the bias is still for a higher dollar/yen rate," he said.
The yen also edged higher on the crosses. The euro fell 0.5 percent to 114.60 yen, pulling away from an 18-month high of 115.995 yen set on trading platform EBS on Wednesday.
Against the dollar, the euro slipped 0.3 percent to $1.3139 , retreating from a two-week high of $1.3300 set on Wednesday, with one trader saying that stop-loss selling helped add to the euro's decline on Thursday.
The yen had tumbled on Wednesday after U.S. lawmakers passed a bill on Tuesday to avoid the "fiscal cliff", bolstering investors' appetite for risky assets.
The yen has also taken a hit from expectations that a new Japanese government led by Prime Minister Shinzo Abe would push the Bank of Japan into more forceful monetary easing to beat deflation.
With a number of potentially yen-bearish events coming up over the next few months, including the Bank of Japan's policy meeting on Jan. 21-22 and a forthcoming change in BOJ leadership, the dollar is likely to head higher versus the yen, said a trader for a Japanese bank in Bangkok.
To be sure, since the dollar's recent rise against the yen has been surprisingly fast, there is also a risk that the speed of any pull-back in the dollar could be rapid, the trader said.
"But that is basically a risk scenario, and while the dollar could see a dip of one yen or so, I think it will probably overcome such declines and keep heading higher," he said.
The dollar climbed 12.8 percent against the yen in 2012 for its biggest yearly percentage rise since 2005.
The bulk of those gains came late in the year, with the dollar having risen more than 10 percent versus the yen from a trough hit in early November.