Step 1Using a paring knife or vegetable peeler, cut the peel off the lime in thin strips, taking care to remove only the green and none of the bitter white. Place the strips in a medium saute pan and add the sugar and allspice berries. Add half a cup water and stir to blend. Bring to a boil, then reduce the heat and simmer 5 minutes.
Step 2Using a slotted spoon, remove and discard the lime zest and allspice berries. Stir in the rum, the bitters and 1 tablespoon of juice from the lime (reserve the remainder for another use). Simmer 30 seconds.
Step 3Lower the heat and gently stir in the fruit. Cook 5 to 7 minutes, until the fruit is heated through but not falling apart. Remove from the heat and let cool 5 minutes before serving.