Place cucumbers in a colander. Toss with salt, and let stand 30 minutes.
Meanwhile, combine water, vinegar, sugar, bay leaf, and allspice berries in a medium saucepan, and bring to a boil. Remove from heat, and let cool.
Rinse salt off cucumbers, and squeeze out as much moisture as possible with your hands. Transfer cucumbers to a nonreactive container with a tight-fitting lid, and pour pickling liquid over them. Cover, and refrigerate at least 3 hours before serving.