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Why are some CLIs instant while other times people receive a message that says the credit card company will get back to them in a few days? Does that request get forwarded to someone for a manual review?
Lenders vary in their practices. I don't think broad generalizations will be very accurate.
Instant CLIs are done by the computers. Based on the programmed algorithms, the computer either grants a CLI immediately, denies immediately, or sends you into "the queue" (and you get the 7-10 day or whatever message). Typically when that happens, a human looks it over and makes the final decision. Sometimes if you call you can get some eyes on it faster.
As for what the algorithm looks for, it probably varies from lender to lender, but things I'm sure that are checked include payment history, payment patterns (minimum vs. PIF), average utilization, age of the account, time since last CLI, amounts charged and paid vs. limit, info on your credit report (from the SP or HP), phase of the moon, shoe size, etc.
My answer is always a denial when I get that message from Cap 1. That started happening when my total CL between all of their cards reached $50K. The reason they provide is my scores aren’t high enough for an increase (740-753). I’ve tried for two CLIs from Discover since I received the card in February. I received the we’ll get back to you message both times. Then found a $500 increase a couple days later.