The painstaking work of speeding up Denver’s government service — whether cutting waits at the Department of Motor Vehicles, adopting pets from the animal shelter more quickly or processing food-assistance applications sooner — is about as unsexy as it gets.

Employees spend hours brainstorming ways to cut down on paperwork.

They run simulations to streamline how they push that paper around the office and enter information into computers.

And they figure out how to untangle the convoluted ways government often does things.

Are you still here? Consider this: These seemingly tedious exercises, run by a city program responsible for making government more efficient, have helped the city’s business licensing counter cut average waits from an hour and 45 minutes — and 3 hours at peak times — to less than 20 minutes. The city’s human resources staff fills open positions citywide in 45 days on average, nearly twice as fast as it used to, while the wait to register a vehicle at the DMV is 20 minutes on average, down from 80 minutes several years ago.

And pets sit in cages in the city’s animal shelter for only seven days on average, half the time it took to adopt them out three years ago.

The Denver Peak Academy, which applies the same kinds of efficiency analysis used in the corporate world, has tracked an estimated $9 million in hard savings, either returned to city coffers or banked for other uses. And the city finance department says nearly twice that amount has been saved in workers’ time (an estimated value of $16 million), which allows them to help more customers at the counter — reducing wait times — or on other tasks.

Mayor Michael Hancock, Peak Academy director Brian J. Elms and more than 100 employees from departments and offices helped by the program gathered at an event Thursday to mark its fifth anniversary.

“What’s happening here is that you’re making government better,” Hancock said in the atrium of the city’s Webb administration building. “And we’re all becoming better for our customers.”

The program now has nine employees, including several analysts, and a $1.2 million annual budget. The city estimates that 6,500 employees — just over half — have gone through training ranging from four hours to five full days. (When done, they’re called “green belts” and “black belts,” respectively.)

The Peak Academy has gained attention far outside Denver, with the program drawing participants from 150 cities, from Kansas City, Mo., to Brussels. The program receives compensation in those cases, officials say.

To be sure, Denver’s city offices aren’t all humming like checkout lines at Target.

On the same day as the Peak event, a program that got some of its attention this year — the building permit counter in the planning department — was knocked by City Auditor Tim O’Brien’s office for too-long waits to see a plan reviewer. That counter has seen foot traffic skyrocket during the building boom, and Elms says big leaps will take time.

Here are a few more parts of city government that have improved, according to the Peak Academy:

Fleet Management: The largest hard savings — $5 million — came out of this Public Works agency, which worked three years ago with its heaviest users in the police, fire, sheriff and parks departments. The city standardized more city vehicles, sped up the process to get replacement cars into service and joined a larger purchasing pool that’s used to buy vehicles in bulk.

“We got together with the state to do it,” Elms said.

Food assistance: Peak worked with Denver Human Services staffers for six months to streamline the processing of applications for food stamps and other assistance, which had taken five or six days and 29 stops for each one. Now it takes no more than a day.

Home inspections: A recent project has looked at part of the public health inspections team’s caseload, which numbered 320 open housing complaints. It took 172 days to close the average case. After standardizing each investigator’s approach and tracking cases more closely, the team has 152 open cases, and it takes an average 74 days to close them.

“Those standards of work just helped us process things a lot faster,” said Antonio Pasquarelli, an inspections team member who was on hand Thursday.

Hancock ordered Peak’s creation early in his first term, when the budget still was tight post-recession. Even though savings attributed to Peak pale in comparison to the city’s spending, which was budgeted at $1.9 billion this year, Hancock says the program has beat his expectations.

But shouldn’t Denver’s government be more efficient to begin with?

“The reality is that we don’t earn our money by producing widgets — we earn our money from taxpayers, and so we don’t have to do anything as employees to particularly produce those monies,” Hancock said. “And so you don’t have that tie-in, that ownership (that private-sector employees have).

“But when you give them ownership of their jobs — and you say, ‘We’re going to measure you by your effectiveness and your innovativeness’ — then it changes the whole shape.”