Heat the water and sugar together until the sugar has dissolved. Let cool down. Rinse and dab the herring fillets. Peel and slice the onion and carrot, then place in the sugar solution.
Add the bay leaf, crushed allspice and vinegar essence, stir. Put the herring fillets in a sealable container, pour the vinegar solution over them. Chill for 2 days.
Remove the herring fillets from the vinegar solution (strain and save the liquid!) And cut into pieces. Put in a bowl. Add the red onion slices and allspice, pour about 1/3 of the marinade over it.