The Foreign Office says it will in future be more selective about issuing travel advice on the risk of terrorism.
Mr Straw said too many warnings "did the terrorists' work for them"
From now on, people will be warned against travelling only in situations of extreme and imminent danger, Foreign Secretary Jack Straw said.
He said blanket warnings against travel to an area would be used only when the threat to British citizens looked "acute, large-scale and specific".
Too many warnings "did the terrorists' work for them", he added.
The FO says new rules have been drawn up to strike a balance between likely danger and the disruption caused by warning about the possibility of terrorism.
The move is likely to be welcomed by foreign governments like Turkey and Kenya.
They had complained that warnings issued after terrorist attacks had compounded their misery by seriously damaging their tourist trade.
At the end of last month, officials advised Britons against all but essential travel to Saudi Arabia because of fears about attacks on oil and western targets in Saudi Arabia.
The warning came after a British oil executive was shot dead by gunmen during a hostage siege in the city of Khobar that killed at least 22 people.