Preparation

1. To form the pizza crusts, sprinkle a work surface with flour. Using a rolling pin, roll the pizza dough into 8- to 10-inch circles or free-form shapes that are 1/8 inch thick. Be careful not to break the dough. If the dough shrinks as you roll it out, cover it with plastic wrap and let it rest for 15 minutes, then try again. Stack your finished rolled-out crusts between sheets of floured parchment paper or plastic wrap and cover the stack to prevent drying out.

2. Assemble your pizza toppings. Use relatively dry toppings to prevent soggy pizzas, and use a thick tomato sauce or well-drained chopped tomatoes. You should also forgo raw vegetables such as mushrooms or bell peppers, which will give off water as they cook. Instead, use roasted vegetables, sauteed mushrooms and dry, flavorful cheeses such as parmesan, crumbled ricotta salata and bleu. Pungent bleu cheese works wonderfully with sweet elements, such as grilled fresh figs.

3. Choose a wood. Mesquite wood chips impart a mild and sweet smoky flavor to grilled foods. This makes them a good choice for pizza. Wine barrel chips are another suitable option. Smokier woods, such as hickory or oak, may overpower the pizza.

4. Prep the wood. For a charcoal grill, use wood chunks. Soak 2 cups or more in warm water for one hour before using. For a gas grill, use 2 cups wood chips. Soak chips in warm water for 30 minutes, and then put them into an aluminum foil packet with perforations that allow air to circulate.

5. Heat th egrill. For a charcoal grill, make a medium-hot charcoal fire, spreading the coals over three-quarters of the surface to create a hot spot and a smaller cool spot. When the coals are hot, place the wood chunks directly on the coals. Add the grate and heat for five minutes. For a gas grill, put the packet containing wood chips over the burner, turn the grill to high and heat until very hot, which will take about 15 minutes.

Grilling

1. Carefully transfer the pizza crust to the grill using the pizza peel or cookie sheet. If using charcoal, place it on the hot section of the grill. The crust should immediately cook on the bottom and it may puff up. Check the crust constantly, as it will cook in only one to three minutes and the crust can burn very quickly. If the crust begins to burn on your charcoal grill, quickly move it to the cool spot. When the bottom of the crust is firm with grill marks and small charred blisters, grab it with tongs and remove it immediately.

2. Brush the grilled side of the pizza with sauce or flavored olive oil. Add other toppings and cheese, using a light hand. A light sprinkling of flavorful cheese will work better than a heavy blanket of mozzarella.

3. Return the pizza to the grill. For charcoal grills, use either the cool spot or the hot spot to get the right amount of heat. Close the grill lid briefly for enveloping heat, but also keep a constant eye on the pizza. Shift it around on the grill if necessary to promote even cooking. When the bottom shows grill marks and the cheese is melted, remove pizza with the peel or sheet. Top it with arugula, slivered fresh basil or other fresh toppings.