There are some truly terrible classic vehicles out there, whether we’re talking about luxury models with high maintenance costs, sports cars that are difficult to live with on a daily basis, or automobiles compromised by puzzling design choices that haven’t aged well. While the most notorious models are well known, there’s a surprising overlap between some of these purveyors of painful ownership experiences and the object of many enthusiasts’ desires.

Whether it’s a case of being blinded by the beauty of the design, enthralled by the vehicle’s capabilities, or simply blown away by its potential for performance, there are a surprising number of truly “heartbreaking” cars out there that we all still want to own. Here are five of the most intriguing offenders that generate pulse-quickening passion and code-blue palpitations even as they ask us to overlook their pitfalls before parking one in the garage.

1993-1995 Mazda RX-7 FD

Why we love it: Has Japan ever produced a more gorgeous car? The final-generation FD RX-7’s flowing sheetmetal and pop-up headlights represent a high bar for ’90s styling that still manages to look contemporary more than 30 years after its debut. Then there’s the fact that this lightweight (less than 3,000 pounds) sport coupe is beautifully balanced and features a sequentially turbocharged Wankel rotary engine that nears 8,000 rpm at full throttle in search of its 255 horsepower and 217 lb-ft of torque.

There’s truly nothing like it on the modern market, and it represents that brief sliver of time when Japan’s bubble economy was pushing a dizzying array of high-tech, near-supercars onto the American market at a breakneck pace.

Why it will break our hearts: About that rotary engine. You see, there’s nothing inherently wrong with the RX-7’s drivetrain, it’s just that swapping pistons for a Wankel’s spinning rotors pushes you through the looking glass when it comes to this Mazda’s ownership experience. Say goodbye to nearly everything you know about maintaining a traditional internal combustion engine, and say hello to carefully observed warmup routines (up to 10 minutes of idle to get up to temp, then a few minutes of easy driving after a cold start), to oil consumption (a ‘feature’ designed into every rotary engine), to apex seal replacement (a non-trivial job), and to heat damage suffered by every plastic or rubber tube, hose, or clamp in the engine bay primarily due to the turbo system.

Then, of course, there are the must-do reliability mods, like replacing the pre-cat, dumping the ready-to-crack air separation tank before it bathes the engine in coolant, and swapping in an all-aluminum radiator for the original one with the brittle plastic end tanks. None of the above is terminal, but you’ll be lucky to find a rotary expert in your area without a three-year waiting list. This RX-7 is perhaps the only car in this story that requires you to adopt an entirely new lifestyle just to support and feed it in the manner it requires.