Delta Air Lines says its effort to up-sell customers on more expensive fares is succeeding, with more passengers booking higher-priced economy and first-class seats.

The airline’s tiers of “branded fares” — presented as options to customers when they use Delta’s website — boosted revenue by $56 million in the second quarter, Delta said Tuesday.

The tiers include Basic Economy with no advance seat assignments and less flexibility; Main Cabin as the standard economy fares; Delta Comfort+ for coach seats with more legroom; First Class, and Delta One international business class.

About 65 percent of shoppers opt out of Basic Economy and choose the higher Main Cabin fare, Glen Hauenstein, Delta’s executive vice president of network planning and revenue management, told analysts during a conference call on Delta’s second-quarter financial report.

“What we’ve seen is a very high up-sell rate from that,” Hauenstein said. “Most people are opting not to take that fare, but to take the next higher fare, which is essentially an added-on price.”

Delta said the percentage of first-class fliers buying a seat, as opposed to using a free upgrade, has jumped from 13 percent to 57 percent, with the company goal of 70 percent. But for frequent travelers, that decreases the chance of upgrades.

Delta executives discussed results with the fare tiers as the Atlanta-based carrier reported a profit of nearly $1.5 billion in the second quarter.

One weakness has been a recent decline in unit revenue, or the amount generated by each seat, which Delta blamed on international pressures and “pockets of domestic weakness.” The airline, which grew capacity by 3 percent in the second quarter, plans to scale back growth in the latter part of the year.

That “should put the business on the right trajectory to stem the erosion in unit revenues by the end of the year,” Delta President Ed Bastian said in a written statement.

The Justice Department recently launched an investigation into whether Delta and other airlines are colluding by coordinating on capacity growth, which can keep fares higher.

On Wednesday’s conference call, Delta CEO Richard Anderson defended the company’s “transparency to investors” in discussing growth plans.

“We are going to continue to comply with the law, act unilaterally and do our best to give our investors visibility into our business,” Anderson said.

Separately, Anderson said Delta will cancel plans to buy 20 Embraer E190 planes and 40 more Boeing 737-900ER planes that had been contingent on a new pilots labor contract, which the pilots voted to reject last week. Negotiations will resume on a deal to replace the current contract, which runs through this year.