Combine fruit, sugar, and lemon juice in large bowl. Let stand at room temperature 2 hours, stirring occasionally.

Put 2 saucers in freezer.

In bottom of heavy large stockpot at least 3 inches deeper than height of jars, place metal rack or extra screw bands from canning jars to protect jars from direct heat. Fill pot with water, cover, and bring water to boil. Reduce heat to low. Wash jars, lids, and screw bands in hot soapy water; rinse well. Set screw bands on clean towel to dry. Place lids in small saucepan; cover with cold water and bring to simmer; turn off heat. Fill jars with very hot water.

Transfer fruit mixture to large saucepan and bring to boil over med-high heat, stirring occasionally. Mash to thick puree with potato masher. Reduce heat to medium and boil gently until mixture begins to thicken, stirring often, about 18 minutes.

Remove saucepan from heat to test jam for gelling point. Drop 1 teaspoonful jam on chilled saucer and return to freezer 1 minute. Remove saucer and push edge of jam with fingertip. If jam has properly gelled, surface will gently wrinkle. If not, return saucepan to heat and cook jam a few minutes longer; repeat test.

Drain hot water from jars and shake out excess water. Place jars on cutting board, Ladle hot jam into each jar, leaving 1/4-in space on top. Slade flat plastic spatula between jam and jar to eliminate air bubbles. Clean rim of each jar with damp cloth. Using tongs, lift hot lids from saucepan, 1 at a time, shake dry, and place atop jars. Seal each with screw band, twisting to close but not too tightly. Return filled jars to pot of hot water.

Add water to pot, if necessary, to cover jars by at least 1 inch. Cover pot and bring to boil; reduce heat and boil gently 10 minutes. Turn off heat. Wait 5 minutes; use tongs to remove jars without tilting. Place upright on towel; cool completely at room temperature. Jam with thicken as it cools.

Check lids for seal by pressing each lightly. Lids of sealed jars will be concave and show no movement when pressed.

(For peach or apricot jam, use 2 pounds fruit, 2 cups sugar, and 2 tablespoons lemon juice. Rinse, dry and rub any fuzz off peaches, if using. Halve, pit, and cut fruit into 3/4-in pieces. Place in bowl and toss with sugar and lemon juice, then follow directions above.