Mendeb Three was a planet in the Mendeb system.
Mendeb Two and Three were colonised by the TAM Corporation. During a galactic war, they abandoned the system, and connected the two planets with a space station and a communication system.
The Second Doctor unwittingly severed contact between the the two worlds, giving the Duke Vethran the chance to take over Mendeb Three.
The Seventh Doctor and Ace returned many years later during the 30th century and discovered that the Duke was kidnapping people from Mendeb Two, giving them the mind control drug SS10, then selling them as slaves. Ace eventually gave the drug secretly to Vethran, removing his free will permanently. The Doctor and Ace left the people of both planets to establish peaceful relations. (PROSE: Independence Day)