Honor doubles/Rosenkranz double

After partner has overcalled, and RHO has bid another suit, responder may double to show support plus one of the top three honors in partner's suit.
A single raise shows support but no top honor.
A cue bid shows support, no top honor, but limit raise or better values.
A double raise is preemptive and may or may not show an honor, depending upon partnership agreement (Usually does).