Peel, pit, and finely chop or crush enough ripe peaches to measure exactly 4 cups after preparation.

Wash five half-pint jars, lids, and bands. Keep the jars hot while preparing the jam, and use new lids for shelf-stable processing.

Combine the peaches, bottled lemon juice, powdered pectin, and optional butter in a large, deep saucepan. Bring to a full rolling boil over medium-high to high heat, stirring frequently.

Add all 5 cups of sugar at once and stir constantly until dissolved. Return the mixture to a full rolling boil and boil hard for 1 minute, stirring constantly.

Remove the pan from the heat and skim away foam if needed. Ladle the hot jam into hot jars, leaving about 1/4 inch headspace.

Wipe the jar rims, apply the lids, and screw on the bands fingertip-tight. Process sealed jars in a boiling-water bath for 10 minutes, adjusting for altitude and following the pectin manufacturer's directions.

Let the jars cool undisturbed for 12 to 24 hours before checking the seals. Refrigerate any unsealed jar and use it promptly.