Barclays is very tough. I have no problems with any other card issuers but Barclays. I applied for their Arrivals card numerous times but denied every time (too many inquiries or max credit).

So recently, I applied for the US air (also offered by Barclay) with the annual fee, and was quickly approved. The miles are still worth the annual fee, so actually, I was fine and quite happy about the approval. Still, I have a hard time cracking one card, let alone 3. (I tried calling reconsideration once; they are hard to budge, so good luck)