I agree with the guys above. Don't cancel it. use it as leverage. I did it earlier with 2 approvals. Although they were business cards.

I have a Southwest Business Chase card. I applied for 2 more cards.
1. Chase Ink Bold Charge Card
1. Chase Ink Plus Credit Card.
They approved my Ink Plus without a problem, but I had to talk to a rep over the phone for the Ink Bold.

She said I had to lower my credit limit in order to get the Ink Bold.

This is slightly different than your situation only because of the charge card (and it's business).