Rinse the currants, drain well, and remove from the vines. Add the currants, 150 ml (approximately 5 ounces) of water, and the vanilla sugar to a saucepan. Mix well, and bring to a boil. Reduce the heat and simmer for 15 minutes (or until the berries burst), stirring occasionally.
Line a fine strainer with cheesecloth. Place the strainer over a large pot, and pass the fruit mixture through strainer. Drain slowly, and let cool completely. Squeeze the mixture in the cheesecloth to extract all the juice.
Measure the juice. Add the appropriate amount of jam sugar (it should be a 2:1 ratio of juice to sugar), then mix until combined. Bring to a boil, and cook the mixture for 4 minutes until the jam begins to thicken. Skim any foam that rises to the surface.
Fill the prepared jars to the brim with the jam. Seal tightly and turn upside down to cool slightly. Turn right side up and cool completely.