Allow cooked rice to cool to room temperature and transfer it to a medium bowl.
Meanwhile, in a food processor fitted with a chopping blade, process the crab until it is very finely chopped and starts to stick together. Transfer it to a medium bowl and stir in the mayonnaise.
In a small bowl, stir the sugar and salt into the vinegar until it is dissolved. Hold a wooden spoon over the bowl of rice and pour vinegar so that it runs down the spoon and is evenly distributed over the rice. Then stir the mixture. The rice should be sticky.
Next, place a sushi mat on a work surface so that the wooden sticks that comprise it, run horizontally. Place one sheet of Nori on the sushi mat. Run your hands under cool water then scatter about ¼ of the rice (about 1 cup) evenly over the Nori. Then press the rice in a thin even layer firmly over the Nori so it is completely covered. (Remoisten your hands slightly if the rice starts to stick to them). Then spread 1/4 of the crab mixture (about a heaping ¾ cup) over about ½ of the rice starting from the edge closest to you. Lay the strips of cucumber or avocado lengthwise on the strip of rice next to the crab. Then pick up the end of the rolling mat and nori closest to you and roll it tightly to the rice on the far side then continue to roll it so that the exposed rice wraps around the stuffed roll. Transfer the roll to a cutting board.
Run a very sharp knife with a thin, straight blade under cold water. Shake off any excess water then slice the roll into 12 equal slices.
Repeat the procedure 3 more times, using the remaining nori, rice, crab and cucumber or avocado.
Makes 4 rolls; 8 6-piece servings:
Each 6 piece serving has: 234 calories, 14 g protein, 39 g carbohydrates, 2 g fat, trace saturated fat, 42 mg cholesterol, trace g fiber, 114 mg sodium
Traditional California Roll (6 pieces) has: 504 calories, 14 g protein, 87 g carbohydrates, 11 g fat, 1 g saturated fat, cholesterol not available, 2 g fiber, 738 mg sodium
Devin Says: You'll be the hit of any party if you bring a platter of California rolls-they're inexpensive, yet impressive and very easy after you practice a few times.
Devin Says: Do not use leftover rice for sushi. It should always be made fresh and cooled, ideally for a couple of hours.
Devin Says: Save money by seeking out an Asian specialty market in your area. Not only will you find tons of unique prepared sauces and foods, key Asian ingredients like sushi rice, wasabi, nori and even Saki tend to be much less expensive when purchased there.