To prepare fruit: Stir together 3/4 cup sugar, cornstarch and cinnamon in a 9- to 10-inch nonreactive deep-sided skillet or 3-quart wide-bottomed saucepan or Dutch oven (see Note). Stir in cranberry (or orange) juice and lemon zest, then the cherries and other fruit. Bring the mixture to a gentle simmer over medium heat, stirring. Simmer, stirring, until the mixture thickens slightly, about 2 minutes. Remove from the heat, taste and add up to 2 tablespoons more sugar if desired.

To prepare dough: Whisk all-purpose flour, whole-wheat flour, 1 1/2 tablespoons sugar, baking powder, salt and baking soda in a medium bowl. Add butter and oil. Using a pastry blender, two knives or a fork, cut in the butter until the mixture resembles coarse meal. Add 3/4 cup buttermilk, mixing with a fork just until incorporated. The dough should be very soft and slightly wet; if necessary, stir in a little more buttermilk. Let the dough stand for 3 to 4 minutes to firm up slightly.

To finish: Use lightly oiled soup spoons to scoop up the dough, dropping it in 8 portions onto the fruit, spacing them evenly over the surface. Return the slump to the stovetop and adjust the heat so it simmers very gently. Cover the pot tightly, and continue simmering until the dumplings are very puffy and cooked through, 17 to 20 minutes. (Cut into the center dumpling with a paring knife to check for doneness.) Let the slump cool on a wire rack, uncovered, for at least 15 minutes. Sprinkle the cinnamon sugar over the dumplings. Serve warm.

Tips: Find frozen, canned and dried sour cherries at King Orchards, (877) 937-5464, kingorchards.com, and The Cherry Stop, (800) 286-7209, cherrystop.com.

Be sure to measure frozen cherries while still frozen, then thaw. (Drain juice before using.)

To pit sour cherries, squeeze them gently until the pit pops out.

Notes: Whole-wheat pastry flour is milled from soft wheat. It contains less gluten than regular whole-wheat flour and helps ensure a tender result in delicate baked goods while providing the nutritional benefits of whole grains. Find it in the baking section of the supermarket or online at King Arthur Flour, (800) 827-6836, bakerscatalogue.com.

A nonreactive pan--stainless steel, enamel-coated or glass--is necessary when cooking acidic foods, such as tomato or lemon, to prevent the food from reacting with the pan. Reactive pans, such as aluminum and cast-iron, can impart an off color and/or off flavor in acidic foods.

MAKE AHEAD TIP: Best the first day, but will keep, covered, in the refrigerator for up to 2 days. Serve at room temperature or reheat to slightly warm in a 250 degrees F oven or microwave.