The day before, make pickles: Pour vinegar and 4 teaspoon salt into gallon-size resealable plastic bag and swish around to combine. Add cucumbers and dill branches; turn several times to coat with mixture. Refrigerate overnight. If and when you pop into the fridge, turn the bag to keep things well mixed.

Cook your potatoes: Although you don’t have to, I also like to boil my potatoes the day before, because I like them very cold, and it seems easier to get it out of the way. Boil them in a large pot salted water until tender, about 30 minutes. Drain, then cool completely. I leave them in the fridge overnight.

The next day: Drain cucumber mixture in a colander; if you’ve got an hour, you can drain it that long, but I never do. Discard brine and dill.

Assemble your salad: The original directions called for peeling your cold potatoes but I never do. Cut potatoes crosswise into ½-inch-thick slices. Place potatoes in large bowl; sprinkle generously with coarse salt and pepper. Add drained cucumbers, onion, sliced radishes, and remaining 3 tablespoons dill; toss to blend.

1 to 2 hours before serving: Stir mayonnaise into salad to taste. Season with additional salt and pepper. Serve cold or at room temperature.

Do ahead: Salad keeps dressed for a day. Salad keeps without mayo for a few days; I add mayo before serving. In both cases, keep it covered in the fridge.