Stir in one cup of sugar plus 2 tbsp of lemon juice and continue stirring the blackberries over low heat. The juices may foam, but continue stirring to keep the foam down. In this low sugar recipe, you may use 1 tbsp of blackberry juice mixed with 2 tbsp of cornstarch to help thicken the jam more quickly. You may also add more sugar to thicken the jam (but it will make the jam sweeter). If you desire the low sugar version, patiently cook the juices down. It may take up to 30 minutes to cook the juices down for this low-sugar version.