Embodiments of a lid covering a device die improving heat dissipation for a die package are described. Trenches are formed on the bottom side of a lid to increase surface area for heat dissipation. Various embodiments of the trenches on the lid are described. The layout and design of the trenches could be optimized to meet the heat dissipation need of the device die(s). By using the lid with trenches, heat dissipation efficiency is improved and the amount of thermal interface material (TIM) could be reduced. In addition, the selection of thermal interface materials for the lid is widened.