Today, lignin from kraft pulping is used mainly as fuel, with only very small amounts being used as raw material for chemicals and materials. This work focuses on using a convenient method for separating large amounts of low molecular weight lignin from the kraft process. Low molecular weight lignin contains larger amounts of phenolic structural units, which are possible modification sites and can be used as antioxidants. Moreover, a product that has reduced polydispersity, low molecular weight, and purified lignin could be a potential material for new applications. The studied process for separating lignin from weak black liquor used a membrane with a cut-off of 1000 Da. During precipitation of the 1000 Da permeate, it is necessary to prevent formation of fairly large, rigid particles/agglomerates of lignin by keeping the temperature low. To improve the dead-end filtration, higher ionic strength is needed for the weak black liquor. Additionally, reducing the end pH will cause more material to precipitate. More sulfur was found in the low molecular weight lignin and at lower precipitation pH, indicating that most sulfur left in the lignin samples might be bound to low molecular weight lignin.