Using a mandoline or sharp knife, finely slice the cucumbers and red onion. Put in a mixing bowl with the dill sprigs and a pinch of salt while you prepare the pickling solution.
In a small pot over medium heat, combine white vinegar, sugar, allspice and salt. Stir well until the liquid is simmering and the sugar has completely dissolved. Pour pickling liquid over red onion and cucumbers and stir to ensure everything is evenly coated. Allow to cool to room temperature, then cover with plastic wrap (press the plastic wrap down onto the cucumbers so there is no air) and refrigerate. Chill for at least 4 hours to cool completely before serving.