Place cucumber slices in medium heatproof bowl. Bring vinegar, sugar, salt, and allspice to simmer in small saucepan over high heat, stirring occasionally to dissolve sugar. Pour vinegar mixture over cucumbers and stir to separate slices. Cover bowl with plastic wrap and let sit for 15 minutes. Uncover and cool to room temperature, about 15 minutes. Pickles can be refrigerated in their liquid in airtight container for up to 2 weeks.

Makes 3 cups