Cucumber Gimlets

Slice four 1/4-inch-thick slices from 1 cucumber. Peel and coarsely chop remaining cucumbers; transfer to processor and purée until smooth. Pour through fine strainer set over large bowl, pressing on solids in strainer. Discard solids in strainer. Mix 1 cup cucumber juice, gin, lime juice, and sugar in pitcher; stir until sugar dissolves. Add ice; mix well. Immediately strain mixture into 4 small Martini glasses. Garnish with lime and cucumber slices and serve.