At the head of Berufjörður, the 19km Öxi mountain pass (Rte 939) offers a summer short cut to drivers en route to or from Egilsstaðir. The pass cuts about 70km off the Djúpivogur–Egilsstaðir journey (compared with following the coastal Ring Road) and gives some gorgeous views, but it's a narrow gravel road and isn't advised in bad weather or fog, or for nervous drivers. Note: the road is closed in winter.
Google Maps and GPS systems may give Öxi pass as the shortest option – which it is, in summer – but it's best to think about the options and not blindly follow directions.