The best time to wrap a brisket during cooking is when it reaches an internal temperature between 160°F and 170°F (71°C to 77°C), typically at the phase known as "the stall" when the brisket's temperature plateaus due to moisture evaporation cooling the meat. Wrapping at this point helps to lock in moisture, speeds up the cooking process by insulating the meat, and helps push through the stall to reach desired tenderness faster. Common wrap materials include aluminum foil, which locks in moisture leading to a braised-like texture but can soften the bark, and butcher paper, which allows some moisture escape and maintains a better bark texture. Wrapping too early can hinder bark formation, while wrapping too late might result in excessive moisture loss. After wrapping and cooking, it's recommended to let the brisket rest wrapped for 30 minutes to 1 hour before slicing to enhance tenderness and juice distribution.