(Down  - Top)  
IBR 11.1 -  Responsive DBL after Partner's Take-out DBL
A double when there has been an immediate raise to the 
2-level or 3-level (of Opener's suit) after Partner's  Take-out 
Double is a Responsive 
Double.
 In Example 1 below South's Responsive Double  shows 6+ 
points and length in both major suits. Partner 
(North, usually with at least 4-3 in the majors) will now bid 
the suit he prefers.
 
S : ♠ K 9 5 2 
    ♥ Q J 8 3   
  ♦ 7 4 2      ♣ 7 6
 South may  be much stronger of course, like 
the hand shown below for example. 
|  1a.  
 | 
| W  | N  | E  | S |  
| 1♦ 
 | DBL 
 |   2♦  
 |  
DBL 
 |  
| Pass 
 | 2♠ 
 |   Pass  
 |  4♠ 
 |  
 
 | 
S : ♠ K Q 5 2 
    ♥ Q J 8 3   
  ♦  4 2      ♣ A 6 3
In this case South goes on to bid Game in 
Partner's preferred suit.
In Example 2 East has raised to the 
3-level. In this case South's Responsive 
Double must be slightly stronger, 9+ points, but 
it still promises length in both majors.
 S : ♠ K 9 5 2 
    ♥ Q J 8 3   
  ♦ 7 4 2      ♣ A 6
In Example 3 South does not bid 
spades, and therefore  denies holding 4 cards in that 
suit.
His Responsive Double in 
this case shows  4-4 in the 2 minor suits,  as well as 
tolerance (2 card support) for Partner's (presumed) spade 
suit.
S : ♠ J 9     
  ♥ 7 5 3     
♦ K Q 4 2      ♣ Q 10  7 6