In a 8 to 10-quart pot with the lid on, soften the fruit over low to medium heat. Lightly smash the fruit with a potato masher. Meanwhile, prepare a water canner. Heat the jars and lids in simmering water until ready for use. Do not boil. Set bands aside.
In a large liquid measuring cup, combine 2 cups of the sugar with the pectin. Add the lemon juice and sugar-pectin mixture to the fruit. Over high heat, bring the mixture to a full rolling boil that cannot be stirred down, stirring frequently with a wooden spoon. Boil for 1 minute. Add the remaining sugar immediately, and bring back up to a hard boil. Boil for 1 to 2 minutes, stirring constantly. Remove from the heat. Skim off any foam if necessary. (or use a vegetable defoamer to dissolve any foam)
Ladle hot preserves into hot jars, leaving ½ inch head-space. Wipe the rim of the jars with a clean, damp paper towel. Center the lid on the jar. Apply the band until the fit is fingertip tight. Process jars in a boiling water canner for 10 minutes, adjusting for altitude. Remove the jars and allow to cool. I use a pair of rubber-tipped tongs to easily grip hot jars Check the lids for seal after 24 hours. The lid should not flex up and down when the center is pressed. Store jars in a cool, dry place.