With European leaders endorsing on Sunday May's plan for future ties between Britain and the bloc, sterling traders are focused on a parliamentary vote on the deal likely to take place in mid-December.
May is seeking to win over critics in her Conservative and opposition parties but the odds look stacked against her with criticism of the agreement approved in Brussels from all sides, including from the Northern Irish party propping up her minority government.
"The failure of the pound to rally on recent positive developments suggest the market is pricing in that the deal won't pass the first time in parliament," said Lee Hardman, a currency analyst at MUFG.
"During the next two weeks the pound will likely trade with increased volatility."
Brexit negotiations and political uncertainty in Britain remain the key drivers for the pound, and many analysts are cautious about its prospects.
The pound traded flat versus the dollar at $1.2821 at 1630 GMT and traded down 0.1 percent against the euro at 88.51 pence.
Recent positioning data suggests hedge funds have started to unwind large short positions on sterling as hopes grow that Britain may manage to negotiate an orderly Brexit.
Net short positions on the pound saw their fourth biggest weekly drop in over a year, according to CFTC data for the week ending Nov. 16.
But growing domestic opposition to May's Brexit arrangement has continued to pressure sterling, pulling it down 2.5 percent from a Nov. 7 high of $1.3176.
"The outcome being priced into GBP right now is the idea of a successful second vote in parliament on the negotiated deal and an orderly exit on March 29," said Simon Derrick, chief currency strategist at BNY Mellon.
Derrick said a "significant financial market reaction" to the failure of the first vote could help concentrate the minds of the politicians that voted against it.
May is embarking on a two-week campaign to sell her plan to the British electorate.
No-one knows what will happen if Britain's parliament rejects the Brexit deal the government has reached with the European Union, she said on Monday. (Reporting by Tom Finn Editing by Robin Pomeroy)
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