BRING boiling-water canner, half full with water, to simmer. Wash jars and screw bands in hot soapy water; rinse with warm water. Pour boiling water over flat lids in saucepan off the heat. Let stand in hot water until ready to use. Drain well before filling.
STEM and crush currants thoroughly, one layer at a time. Place currants in large saucepan; stir in water. Bring to boil. Reduce heat to low; cover and simmer 10 min., stirring occasionally. Place three layers of damp cheesecloth or a jelly bag in large bowl. Pour prepared fruit into cheesecloth. Tie cheesecloth closed; hang and let drip into bowl until dripping stops. Press gently. Measure exactly 6-1/2 cups prepared juice into 6- or 8-qt. saucepot. (If needed, add up to 1/2 cup water for exact measure.)
STIR pectin into juice in saucepot. Add butter to reduce foaming. Bring mixture to full rolling boil (a boil that doesn't stop bubbling when stirred) on high heat, stirring constantly. Stir in sugar. Return to full rolling boil and boil exactly 1 min., stirring constantly. Remove from heat. Skim off any foam with metal spoon.
LADLE immediately into prepared jars, filling to within 1/8 inch of tops. Wipe jar rims and threads. Cover with two-piece lids. Screw bands tightly. Place jars on elevated rack in canner. Lower rack into canner. (Water must cover jars by 1 to 2 inches. Add boiling water, if necessary.) Cover; bring water to gentle boil. Process 5 min. Remove jars and place upright on a towel to cool completely. After jars cool, check seals by pressing middles of lids with finger. (If lids spring back, lids are not sealed and refrigeration is necessary.)
RECIPE COURTESY OF KRAFT FOODS