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More approachable than a stirred Dry Martini and downright soft compared to a Naked Martini.
A Bradford is a Dry Martini which is shaken rather than stirred. Like the Martini itself, the origin of the Bradford is lost in time. However, In Harry Johnson's 1900 edition of his Bartender's Manual he includes two Martini recipes – one simply titled "Martini Cocktail" and the other "Bradford à la Martini" – crucially the Martini is stirred while the Bradford is shaken. This difference is reinforced by David Embury in his 1948 The Fine Art of Mixing Drinks, "If you shake the Martini it becomes a BRADFORD."
In common with his Martini recipe, Harry Johnson's 1900 Bradford à la Martini recipe calls for equal parts "Tom gin" and "vermouth" shaken with "3 or 4 dashes of orange bitters" and "the peel of one lemon". He specifies to garnish with "a medium-sized olive."