In a saucepan bring the water to a boil. Add the salt and boil for 2 minutes. Let cool for 5 minutes. Then add the vinegar and let the mixture cool for several hours.
Wash the cucumbers and dry with paper towels.
Put 1 dill head in the bottom of a sterilized quart jar.
Pack the cucumbers into the shoulder of the jar. Add the garlic and the pickling spices. Cover with the remaining dill. Add salt and water to within 1 inch of the top of the jar and keep partially covered for 2 to 3 days.
When the jar starts to bubble, let it bubble a day or two, removing the scum daily.
Then seal and store in a dry, cool place for about 3 weeks before using.
Refrigerate after opening. The pickles should last several weeks after opening in the refrigerator, or indefinitely unopened.