A camshaft phaser for use with an internal combustion engine for controllably varying the phase relationship between a crankshaft and a camshaft in said internal combustion engine, said camshaft phaser comprising: a camshaft phaser input member connectable to said crankshaft of said internal combustion engine to provide a fixed ratio of rotation between said camshaft phaser input member and said crankshaft; a camshaft phaser output member connectable to said camshaft of said internal combustion engine; a valve spool rotatable relative to said camshaft phaser input member such that rotation of said valve spool relative to said camshaft phaser input member causes said camshaft phaser output member to rotate relative to said camshaft phaser input member; and a rotational actuator configured to selectively rotate said valve spool relative to said camshaft phaser input member, said rotational actuator comprising: a compound planetary gear set centered about a planetary gear set axis and having an input planetary gear set driven by said camshaft phaser input member and an output planetary gear set driven by said input planetary gear set; and an adjusting actuator connected to said compound planetary gear set and being switchable between an idling state and an adjusting state, wherein said idling state causes said valve spool to be rotated together with said camshaft phaser input member in a one-to-one relationship through said compound planetary gear set and wherein said adjusting state causes said valve spool to rotate relative to said camshaft phaser input member through said compound planetary gear set. a camshaft phaser input member connectable to said crankshaft of said internal combustion engine to provide a fixed ratio of rotation between said camshaft phaser input member and said crankshaft; a camshaft phaser output member connectable to said camshaft of said internal combustion engine; a valve spool rotatable relative to said camshaft phaser input member such that rotation of said valve spool relative to said camshaft phaser input member causes said camshaft phaser output member to rotate relative to said camshaft phaser input member; and a rotational actuator configured to selectively rotate said valve spool relative to said camshaft phaser input member, said rotational actuator comprising: a compound planetary gear set centered about a planetary gear set axis and having an input planetary gear set driven by said camshaft phaser input member and an output planetary gear set driven by said input planetary gear set; and an adjusting actuator connected to said compound planetary gear set and being switchable between an idling state and an adjusting state, wherein said idling state causes said valve spool to be rotated together with said camshaft phaser input member in a one-to-one relationship through said compound planetary gear set and wherein said adjusting state causes said valve spool to rotate relative to said camshaft phaser input member through said compound planetary gear set. a compound planetary gear set centered about a planetary gear set axis and having an input planetary gear set driven by said camshaft phaser input member and an output planetary gear set driven by said input planetary gear set; and an adjusting actuator connected to said compound planetary gear set and being switchable between an idling state and an adjusting state, wherein said idling state causes said valve spool to be rotated together with said camshaft phaser input member in a one-to-one relationship through said compound planetary gear set and wherein said adjusting state causes said valve spool to rotate relative to said camshaft phaser input member through said compound planetary gear set.