Halve each cucumber horizontally, then each half vertically in 4 to make 32 pieces in all. Rub them all over with salt and set aside to drain in a colander for 1 hour. In a medium bowl combine remaining ingredients.
Rinse cucumbers with cold water, drain well and pat dry. Taste for seasoning and salt lightly if no salty flavor remains. Toss with dressing. Transfer to a 1-pint jar and cover tightly. Let sit at room temperature for 24 hours before serving. Can be made several weeks ahead and refrigerated.