Support double vs. suit raise after 1m-(1)-1-(2)

Hi all.  I have a question about the use of support doubles to which there doesn't seem to be clear answer.  Suppose you are sitting South and the bidding goes:

W
N
E
S
1
1
1
2
?

In this sequence, your partner, North, has definitively promised you five or more s (for those of you who play agreements that it can be four, just pretend for a moment that you play it as five or more!).

Suppose further that you, South, hold exactly three spades.

At this point, do you raise North's spade bid directly or do you make a support double?

I have heard different answers to this question.  Some seem to say that support doubles only need to be used when your partner could have only four in a suit but you have exactly three, while I have heard others say just make the support double even when partner has shown five or more (to distinguish three-card support from four-card support).

On the one hand, I see a use to distinguishing three-card support (via a support X) versus four-card support (via a raise, if you play it that this requires four)...on the other hand, I could see wanting to take up bidding space right away if a 5-3 fit has been discovered instead of giving West another chance to bid at a lower level.

How do you play this?

In the sequence you've outlined, I would make a support double with exactly three s; Raising the suit myself shows that I have four or more.
In the sequence you've outlined, I consider support doubles to be "off" b/c partner has already shown five or more s anyhow. I would just go ahead and make a raise with three-card support.
Because I don't play support doubles, or for some other reason, I do not see this question as applicable to my bidding system.

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