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Dbl and bid...having opened?

A frequent bidding problem on BridgeWinners goes like this: You have opened the bidding and LHO has overcalled, passed back to you. You are short in LHO's suit and want to defend if partner is trapping, but otherwise you are offshape for a double (e.g. 5521). Do you double anyway?

For example:

South
x
AKxxx
Q10xxx
Ax
W
N
E
S
P
1
1
P
P
?

Should you double with this hand and correct 2 to 2? Such an auction ("double and bid") shows significant extra values when doubling an opening bid in the direct seat and, for most players, the balancing seat. What about doubling an overcall?

The above example is just one of many. How about this one:

South
AJxxxx
xx
x
AKJx
W
N
E
S
1
2
P
P
X
P
2
P
2

Was this the right auction, or did this auction in fact show:

South
AK10xxx
Kx
Ax
Kxx
W
N
E
S
1
2
P
P
X
P
2
P
2

 

Note that these are just examples. My question is general. The context is 2/1, opener an unpassed hand. He doubles-and-bids at the minimum level after an overcall is passed back to him. Should opener be showing extras, or just an offshape hand that wanted to allow for a penalty pass?

Shows extras, not specific about shape
Shows an offshape minimal hand with defense
Depends too much on context (suits bid, vul, etc)
No clear answer, requires an agreement
Other / I don't know

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