Combine the cucumber, onion, red pepper and salt in a large bowl. Cover with a clean kitchen towel and then layer ice cubes on top of the towel. The ice helps to make the pickles crisp. Refrigerate for 4 hours or overnight. When you're ready to make the pickles, discard the ice and rinse the cucumber, onion and red pepper. Drain well and rinse again. Drain well.

Bring the remaining ingredients to a boil in a stockpot, stirring to dissolve the sugar. Once at a boil, add the cucumber, onion and red pepper to the pot and bring the brine back to a boil. As soon as it starts to boil again, start packing the pickles into clean glass jars. Leave about an inch of room in the top of each jar. Fill the jars with the remaining brine so that there is only 1/2 inch of room left. Cover with clean (and sterilized) jar tops and secure with the screw lids.

Store the pickles in the refrigerator for 3 to 4 weeks. If you want to store them at room temperature for longer, you can can these pickles using the water bath canning method.