Peel and then slice the cucumbers ⅛ to 3/16-inch thick.Fill a one-quart jar with cucumber slices up to the very top.
Combine water, sugar, vinegar, allspice and salt in a medium saucepan. Over MEDIUM heat, bring vinegar mixture to a simmer, stirring just until the sugar has completely dissolved.Remove the prepared brine from the heat.
Use a measuring cup with a pour spout and/or a canning funnel to carefully pour the prepared brine over the cucumbers.
Put a lid on the jar and refrigerate until brine has completely cooled; preferably overnight.
Notes
If the cucumber slices are any thinner than ⅛-inch, the quick pickles will lose their tugor (i.e., crispiness) too fast. If they are thicker than about 3/16 inch, they don’t absorb the brine as quickly.Swedish Cucumbers be stored in their own brine in the refrigerator. They are best eaten within the first week; after that, they will begin to lose their signature crunch.