So yesterday I sent a SM to Chase asking to reduce the credit limit on my Disney Premier Visa to $4k and to product switch to the no-fee version, which I've been meaning to do since forever.* They responded saying they can't do PCs via SM ("call the number on the back of the card") but they could do the limit reduction, which they did. Then today I called the number on the card to do the PC, and was told .. .. .. .. you can't PC unless the card has at least $5k in credit limit. I'm not kidding.
BUT, the rep was very helpful, and said she could just transfer $1k in limits from one of my other Chase cards to the Disney and then apply the product downgrade, which she did. So I'm glad I didn't already lower the limits on my other Chase cards.
* I think the reason it took me so long to do this is I'm just fond of the card. Though it doesn't provide good value, it has that Disney connection, and it was probably my gateway card that started me looking for value back from cards and made me wiling to pay a fee to get a SUB and a better return on spend. It also helped that the fee is pretty low as annual fees go. But still, there was no need to keep paying it as I get better return on spend for every category for which it has the 2% return..