* Sterling up 1.7 pct vs dollar this week
* Bulls still nervous as May prepares for third vote
* Graphic: World FX rates in 2019 tmsnrt.rs/2egbfVh
* Graphic: Trade-weighted sterling since Brexit vote tmsnrt.rs/2hwV9Hv
LONDON, March 15 (Reuters) - The British pound rose on Friday, posting its best week since January, as Prime Minister Theresa May tried to convince eurosceptics to back her deal to exit the European Union in a third parliamentary vote next week.
Sterling has rallied 1.7 percent against the dollar this week after British lawmakers voted against leaving the EU without a deal and backed a delay to the March 29 exit date.
The vote against a no-deal Brexit was non-binding but investors believe Britain will now avert a disorderly EU exit that would severely damage its economy.
May plans to hold another vote on her deal next week although lawmakers have already rejected it twice. She hopes to use the threat of a longer delay to Brexit to persuade eurosceptics in her party to back her.
The Northern Irish Democratic Unionist Party, which May depends on for a majority in parliament, said it is in talks with the government, which is trying to convince its lawmakers to support the prime minister.
The pound, which has traded between $1.2945 and $1.3380 this week, rose 0.4 percent to $1.3294 in late London trading. It also strengthened against the euro, reversing earlier losses to add 0.2 percent to 85.245 pence per euro .
Jane Foley, currency strategist at Rabobank, said sterling traders currently had a “glass half full outlook” when looking at Brexit developments.
She said Friday’s rise was also down to some adjusting of positions, with traders likely reluctant to get caught out should sterling-positive news break over the weekend.
BNP Paribas economists noted that the market had already “shifted significantly to price out a no-deal Brexit.”
The bank’s analysis shows short sterling positioning has unwound to +10 from -33 at the beginning of the year. A -50 reading marks the biggest short position possible, +50 the largest long.
The bank also noted the probability of a rate increase this year had risen to a current 50 percent from 24 percent in February, according to money markets.
“As this suggests markets may be vulnerable to any downside surprises, we do not yet see attractive risk/reward to enter structural long GBP or bearish UK rates outright positions,” BNP Paribas analysts wrote.
However, there is still plenty of uncertainty surrounding the pound. All 27 EU member states must agree to a request for a Brexit extension, while it remains unclear when and on what terms Britain will leave. (Reporting by Tommy Wilkes, editing by Larry King and Kirsten Donovan)