In a saucepan combine water and sugar. Bring to boiling, stirring to dissolve sugar. Remove from heat. Cool about 30 minutes. In a 2 quart square baking dish, combine sugar mixture, lemon juice and tarragon. Cover and freeze 7 hours or till nearly firm.
Break the frozen mix into small chunks. Move to a chilled large bowl. Beat with electric mixer on medium speed until fluffy but not melted. Return mix to the 2 quart dish and cover, freeze at least 3 hours or until firm.
To serve, let stand at room temperature for 10 minutes. Using a large spoon, scrape across the surface and spoon into pretty dishes.