A smoke-diffusing accessory designed to function with a barbecue, the smoke-diffusing accessory forming a container that can contain smoke-generating materials, wherein the smoke-diffusing accessory includes a lid which engages with the container to form a closed enclosure, the lid including calibrated holes so as to regulate the supply of oxygen into the enclosure, and the smoke-diffusing accessory including a suspension system for vertically suspending the smoke-diffusing accessory in the barbecue such that the calibrated holes are oriented upwards.