Speaking to the House Armed Services Tactical Air and Land Forces Subcommittee this week, Air Force Lt. Gen. Christopher Bogdan told legislators that the aircraft suffers from a “perception problem” and an “information gap.”

“The public perception and the reality are so different,” said Bogdan, the Pentagon’s F-35 program manager. “Getting out there and telling the story is part of what we need to continue to do.”

The F-35 Joint Strike Fighter is arguably the world’s most sophisticated fighter jet, laden with advanced sensors, the latest in airborne stealth capabilities, and eight million lines of computing code. With a program cost of $400 billion—and a projected lifetime cost of $1 trillion—it is easily the most expensive weapons system in history.

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It’s also years behind schedule, billions of dollars over budget, and the object of relentless scorn from the media, critics in Congress, and armchair generals alike. A slew of technical setbacks–ranging from engine fires to cracked fuselages to an emergency ejection system that might be just as deadly as a fiery plane crash–have created a long string of rapid-fire PR headaches for the Pentagon and Lockheed Martin (LMT), the aircraft’s manufacturer.

Perhaps the toughest hurdle the Pentagon faces in rebranding the F-35 is that many of its biggest problems aren’t perception problems—they’re quite real. Originally slated to enter service in 2012, only the Marine Corps version has currently been declared combat-ready and even that initial operating capability has been called into question by critics. (The Air Force Plans to declare initial operating capability for its F-35 variant later this year.)

The delays and cost overruns stem from no single problem. The escape systems suffer problems that have barred pilots weighing less than 136 pounds from flying the jet. The aircraft’s $400,000 futuristic helmet has required intensive troubleshooting. An engine fire grounded the entire fleet in 2014, while cracks in the fuselage bulkheads, engine mounts, and turbine blades grounded F-35s the year before. Last year, a report surfaced indicating that the F-35 couldn’t compete with an F-16—one of the many U.S. military jets it is supposed to replace—in simulated aerial dogfights.

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More recently, Pentagon evaluators have cited major problems with the F-35’s software, both on the ground and aboard the aircraft. On the ground, maintenance software designed to diagnose problems can’t tell the difference between healthy parts and defective ones. In the air, a communication glitch between the F-35’s radar computer and its central computer cause the radar to switch off roughly every four hours of flight time, requiring pilots to reboot it.

Though the Pentagon claims these problems are all fixable, the litany of issues plaguing the F-35 over the years—and the high costs associated with them—hasn’t buoyed the F-35’s public image. But since 2010, the program has largely stabilized with production increasing (something like 170 jets have now been delivered to the U.S. and allies) and costs falling.

That’s the story the Pentagon wants to tell with its summer roadshow. As production ramps up and economies of scale begin to kick in, the price of procuring F-35 aircraft over the life of the program is down $7.5 billion in 2012 dollars, Bogdan revealed this week.

“We had real decreases in real costs this year,” Bogdan noted at a press briefing following his remarks to Congress. “For a program that has a tragic past, that is not a bad year.”

To highlight that not-bad year, F-35s will make appearances at more than a dozen public events starting at Luke Air Force Base in Arizona next week. Chicago and New York will both get to see F-35s on the wing. In July, the jet will make a much-anticipated debut at the Farnborough International Air Show and Royal International Air Tattoo, one of the world’s largest and most prestigious aerospace events.

The F-35’s Farnborough debut was originally slated for 2014, but its appearance was canceled when the entire fleet was grounded following that aforementioned engine fire. With rebranding top of mind, the Pentagon is hoping the F-35’s 2016 world tour will run a bit more smoothly.