Negative Doubles are used primarily after your partner has opened and your RHO overcalls.

The most frequent use of the negative double is to show a four card holding in one or more unbid major.  **However, a negative double also is correct with five or more cards in a major when the hand is not strong enough to bid the suit directly.
In the examples below we assume that a new suit at the 2 level in a constructive auction, shows 10+ HCPs.

USE OF NEGATIVE DOUBLES

Partner	RHO	You
*1D	1H	X	=	6+ HCP and four spades . A bid of 1S promises five spades
**1D	1S	X	=	6+ HCP and four hearts or five with insufficient pts. to bid 2H naturally
1D	1S	2H	=	10+ HCP and five hearts (as it would without the overcall)
1H	2C	X	=	6+ and four spades. Can stand partner rebidding 2H  A rebid of 2S by partner would NOT be showing reversing values.
1S	2C	X	=	6+ and four hearts. Can stand partner rebidding 2S
1H	1S	X	=	6+ and both minors. Can stand partner rebidding 2H
1D	X	X X	=	6+ HCP and at least 1 four card major. A bid of 1H or 1S shows five.
1H	X	X X	=	6+ and four spades. Can stand partner rebidding 2H
1H	2C	2D	=	Natural, 8+ but NOT four spades. Can stand partner rebidding 2H  Any response of a minor denies four of a major.

* The beauty of negative doubles is that you can now use the interference by opponents to add more clarity to your auction. 

e.g. 1D - P – 1S Your responding bid of 1S could be four or five spades.

After 1D – 1H - X shows four spades.         1D – 1H – 1S shows five!