In one of the many ironies of life in San Francisco, the areas around trash cans are often the filthiest. It’s an all too common site: A receptacle intended to hold garbage is instead surrounded by garbage after somebody has rifled through it for cans, bottles and other treasure, and strewn everything else all over the sidewalk.

There’s a solution to this problem, but unfortunately the Public Works Department doesn’t like it.

They’re called Bigbelly trash bins, and you’ve probably seen the high-tech, sturdy, rectangular receptacles popping up around the city. They’re very hard to break into, so the areas around them tend to stay clean. They’re also big and self-compacting, so they can accommodate five times as much waste as traditional trash cans, meaning overflow is rare.

A garbage can that actually keeps garbage inside? Say it ain’t so! But for Public Works Director Mohammed Nuru, they’re a no-go.

“I’m not a big fan of the Bigbelly — absolutely not,” Nuru said in a recent interview. He said he thinks they’re too expensive and he doesn’t like that they’re leased, rather than purchased.

Nuru’s refusal to make Bigbelly cans the official city trash bin hasn’t stopped them from dotting San Francisco, and trash hauler Recology services them like any other bin.

Various community benefit districts, groups that raise extra taxes from property owners to fund beautification and safety programs, usually pay for the Bigbelly cans. Some, including in the Castro, are managed by a local community benefits district but paid for by the city’s Office of Economic and Workforce Development.

The Union Square Business Improvement District is paying for 25 Bigbelly cans with no city help and says they’ve made a big difference in making the shopping mecca cleaner. No people or rodents have been able to break into them, there haven’t been any leaks or stains emanating from them and vandalism has been lower than for regular city cans.

“Everybody really wants these cans!” said Karin Flood, executive director of the business improvement district. “Trash that goes in stays in.”

In notoriously filthy San Francisco, that’s actually something to brag about.

The cost of the Bigbelly varies by contract. The 20 cans paid for by the city and installed in the Castro and other neighborhoods cost $3,000 per bin per year to lease, with another $15,000 set aside to cover maintenance for all of them.

Union Square paid $317 per can for installation plus $200 per month per can to lease. Ongoing repairs and maintenance have cost less than $200 per year per can, said Robbie Silver, spokesman for the Union Square Business Improvement District.

In working on this column, I started keeping a “trash journal” to document all the filth I saw when walking around the city, but quickly gave up on that idea because it would be like keeping a “broken car window journal” or a “traffic jam journal.” In other words, journaling would be all I’d be doing.

Last month, I scrawled in my notes that I saw a city trash can at Gough and McAllister streets surrounded by trash, including a full dog poop bag, a guacamole container, cardboard boxes, utensils, blue latex gloves, a vodka bottle and a tube of Oral B toothpaste. Perhaps it was the remnants of a really weird party, but whatever it was, it was gross.

“It’s been like that for three weeks,” said Kenny Lee, who visits his mother in the neighborhood regularly and saw me grimacing at the site. “It’s terrible.”

Calls about such sites go to 311, the city’s service portal, and are then relayed to Public Works, which is supposed to clean up 95 percent of the messes within 48 hours. Last fiscal year, which ended June 30, Public Works cleaned just 73 percent of reported messes within 48 hours. Since July 1, they’re up to 79 percent.

Reports of dirty streets and sidewalks have skyrocketed in recent years. The recent low-water mark, according to data from the controller’s office, was 2,635 calls in February 2014. That shot up to 14,323 in August 2017. Response time has naturally slowed with more reports, and Public Works has responded with special alley-cleaning crews, Pit Stop public toilets and the new Poop Patrol to proactively steam-clean feces from sidewalks.

But installing more and better trash cans seems like an obvious response, too. Currently, the city models are either those old-school cement blocks that look like something out of the “Flintstones” or the newer cans, which are dark green, wire mesh cylinders with a smaller removable can inside.

The old ones are very heavy, very ugly and can’t be positioned on hills. And the newer ones are very easy to break into, making their attractiveness for naught since they become the centerpiece of big trash heaps.

So why not give Bigbelly cans a shot? Nuru pointed to a controller’s report from Philadelphia that showed numerous problems with the cans, including that they’re susceptible to graffiti and that their technology sometimes malfunctions. Nuru said they seem like good options now because they’re placed in more upscale neighborhoods with community benefits districts keeping an eye on them.

“Right now they’re in the nice places,” he said. “If we start doing this in some of the more general areas of our city, I think they would be very vulnerable to vandalism. ... I think if you put one of those cans at Eighth and Market, they won’t last, and the contract for the Bigbellys holds the person leasing responsible for the damage.”

Nuru said he does like that BigBelly bins have sensors to tell those leasing them when they’re getting full and need to be serviced. He’s testing similar sensors on the city’s dark green cans so they can signal to Public Works when they’re more than 70 percent full.

“Based on that data, we can start really targeting locations where cans are being frequently broken into or cans are overflowing,” he said.

Still, Nuru knows new cans are needed. He held an in-house design competition in which staffers developed prototypes for a new city trash can, but none were deemed good enough.

“There’s quite a journey from design to reality,” he said with a laugh.

Instead, Public Works plans to issue a request for proposals for a new garbage can design, with an eye toward ensuring they deter scavenging, are easy to maintain, have a small inner can that can be serviced by Recology, are attractive and are not too expensive.

In other words, we’re going to be waiting a lot longer for effective city garbage cans.

But curiously, Bigbellys do have a prominent San Francisco fan: Mayor London Breed who, like Mayor Mark Farrell before her, praised them. On a recent walk around the Castro, she stopped to admire a Bigbelly.

“Oh, cool!” she said, testing the foot pedal that allows people to deposit trash hands-free. “These are the trash cans we need everywhere!”

I agree. Note to Breed: You’re the boss. You can make it happen.

San Francisco Chronicle columnist Heather Knight appears Sundays and Tuesdays. Email: hknight@sfchronicle.com, Twitter: @hknightsf