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Support doubles after 1 (1) 1

After this auction:

1m (1) 1 (2)

If you have an agreement that 1 promises a 5-card suit here (else you'd make a negative double), do support doubles still apply? Or to put it another way, would a 2 rebid by opener promise 4-card support?

Is there any other use for the double on that auction? Penalty seems unlikely, although in this auction:

1 (1) 1 (2)

it's at least conceivable (you might be 5-5 in the minors). And what about these?

1 (1) 1 (1NT)

1 (1) 1 (dbl)

One of the purposes of the support double is to avoid situations where there is a 5-4 fit and neither partner knows it, but on any of these auctions, if I have four of partner's suit, I know we have nine and would likely be willing to compete to the 3-level based on LOTT considerations. If responder has six he'll let me know either way. How valuable is it to distinguish between 3- and 4-card support on this auction?

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