A disposable lid for containers with beverages, especially hot beverages, such as coffee and tea. The disposable lid has an open part where a compartment is created, enabling a person to drink directly from the top of the container, and where the compartment is limited by a floor. One embodiment includes an integrated filter with narrow slits to hinder particles, such as coffee grains or tea leaves from entering the mouth of the consumer of the beverage. Another embodiment includes an arrangement to slow down the beverage flow entering the drinking compartment, and optionally includes a cooling surface for the beverage. The lid may be provided with an auxiliary lid to be attached to reduce the spilling risk to a minimum.