* Dollar/yen falters after touching 29-month high
* Yen regains some ground after previous day's sell-off
* Euro/yen pulls away from previous day's 18-month high
SINGAPORE, Jan 3 (Reuters) - The yen bounced after hitting a 29-month low versus the dollar on Thursday, having come under pressure earlier after U.S. lawmakers forged a deal to avoid huge tax increases and spending cuts, fueling demand for riskier investments.
The dollar fell 0.2 percent to 87.11 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 added.
The yen also edged higher on the crosses. The euro fell 0.4 percent to 114.72 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 0.1 percent to $1.3169 , inching away from the previous day's high of $1.3300.
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.