Much of the media's coverage of Delta Air Lines'(DAL 0.08%) recent changes to its co-branded American Express (AXP -0.62%) credit cards has been about customer complaints. The changes, which seemed largely focused on making it more difficult to qualify for access to Delta Sky Club lounges when traveling, sparked enough backlash from customers that the company will make some further revisions to the program.

But Delta revealed during its earnings call on Thursday that there have been some positive takeaways from the changes, too. First and foremost, customer feedback and resulting behavior surrounding its Delta American Express credit card sign-ups demonstrated a high level of customer loyalty. Nevertheless, the airline still plans to make some adjustments to the program.

Intense loyalty

"[T]here is intense loyalty to Delta," explained Delta CEO Ed Bastian during the company's second-quarter earnings call when explaining one of the main recurring themes in the feedback it's heard regarding its updated SkyMiles rewards program. Indeed, the loyalty is so passionate that Bastian said it's "heartwarming to see."

This loyalty also shows up in the numbers following the program changes. While some headlines in the media about the program changes may make it sound like customers are rebelling, credit card sign-ups are actually trending, according to the company's original plan when they made the changes. When asked if changes to the program could negatively affect demand or lead to a decrease in demand for its co-branded cards, Delta president Glen Heuenstein said: "[I]f anything, since we've announced it, we've seen a shift to higher premium card acquisitions. So I think we're well within, from that perspective, where we thought we'd be."

One way or another, overcrowding must be addressed

The second of two primary themes Delta saw in its feedback was also, in a way, good news. Bastian said that "most everyone also agrees that something has to be done because everyone sees that the premium number of customers that we continue to build are in excess of the premium assets that we have to offer." Put another way: Delta's lounges are overcrowded.

Overall, the spirit behind the company's loyalty program changes may have been correct, but the execution needs some improvement. To this end, management confirmed that changes will still be made to address its overcrowding problem, but the company will try to be more thoughtful about how it goes about doing it.

"We've received a lot of ideas as to different ways to think about it, and you'll be hearing from us in the coming days," said Bastian.

Raising the stakes for the company to execute well on its loyalty program changes, demand for both travel and its premium experiences remains extremely high. Delta's Q2 revenue beat analyst expectations, rising 13% year over year. Its premium revenue increased 17% year over year, outpacing revenue growth in its main cabin seating by five percentage points. Loyalty revenue also rose 17% "on strong co-brand acquisitions and spend growth," Delta said in its Q2 earnings release.