The Imperial II-class frigate was a smaller, less powerful type of Star Destroyer. These vessels had two extensive hangars on both sides of the hull, which accommodated a number of TIE/LN starfighters and support ships and could be used to carry suspicious vessels while they underwent scrutiny.
A Class II Frigate variant.
The ships could perform several tasks, such as patrolling shipping lanes or engaging Rebel or pirate forces. Officers fresh out of the Imperial Academy were often assigned as junior-staff on board these frigates. They were sometimes referred to as "battle cruisers" out in the field.
A known vessel was the Rand Ecliptic, used as a first mission-assignment for Biggs Darklighter at some point before the Battle of Yavin. It was hijacked by some of its crew, after they found the Empire's methods and corrupt military culture unbearable and defected to the Rebel cause. The Imperial II-class frigate seems to have at least one variant, as a ship similar to the Rand Ecliptic chased Generals Jan Dodonna and Roons Sewell during the former's defection, and was subsequently destroyed. This variant had two extra secondary engines perched on each side of the command tower's neck.