Smoke occurs when the oil and drippings from the ingredients fall on charcoal. When you are using a large BBQ grill, you can prevent this by adjusting the place of charcoal. Though it may be difficult to move the charcoal when you are using a small sized BBQ grill. 

For an alternative, we recommend grilling lean meat instead of fatty meat to reduce the smoke. You can also adjust the amount of smoke by avoiding grilling many fatty meats at once.