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Well have you thought about trying to get a CLI online with discover without a HP?
Why don't you apply for the two cards at the same time so that the banks won't see each other's inquiry?
Not instant to the second. It takes some time for the system to request information from the consumer reporting agencies, and some more time for the consumer reporting agencies to update your credit profile. This should take several seconds. So if you cram an application into this time window the bank won't see the inquiry.
Come on! Not like you didn't know the impact of inquiries is often inflated by relatively inexperienced members on this board!