It is located in the Uldale Fells, about 5 kilometres (3 mi) north of Skiddaw, near the larger fell of Great Cockup 1 kilometre (0.62 mi) to the east, and has an elevation of 395 metres (1,296 ft).

Another hill called plain Cockup is about 2 kilometres (1.2 mi) to the south.

The name "Cockup" derives from the words in the Old English language for a secluded valley and Black Grouse.

There is a circular stone ledge near the top of the fell and on the summit is a cairn with common heather growing around it.

[4] In 2011, Business Weekly published a news story suggesting that the Government of the United Kingdom's Department for Business, Innovation and Skills' Technology Strategy Board was considering investing in nearby towns and the area around Little Cockup.