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2 mm rounds — a dime's thickness — with a keen knife, or a mandoline set thin but NOT at its finest

cucumbers into even rounds, after peeling the skin away in lengthwise stripes if you want the striped shima-muki look, which also lets a little of the skin's bitterness out. Two millimetres is the target because that is thin enough for the vinegar to penetrate the whole slice and still leave it stiff enough to snap; a thick round never takes up the dressing, stays watery in the middle and tastes of almost nothing. The edge decides this. Cucumber exposes a dull blade more plainly than any other vegetable — a blunt edge crushes and tears the round rather than parting it, so the slice comes off the knife ragged and already weeping, and a torn round cannot survive the squeeze this recipe depends on. The finest mandoline setting causes the same failure from the other direction: slices that fine disintegrate in the hand. If the blade is skidding across the skin instead of dropping through it, that is the problem, not your technique.