First they came for the offices, replacing four-walls-and-a-door situations with desks in cubicles, even for workers of considerable stature.

Now they’re coming for the desks themselves.

On both sides of the Atlantic, big companies are moving toward more flexible setups that do away with assigned workstations. The financial motivation to make the most of premium office space is primary. But another big driver now, and going forward, is mobility.

More people are working remotely now, creating workstation vacancies that irk the people paying the rent. But there’s more to it than that, according to Jennifer Busch, vice president of architecture and design at office furniture maker Teknion.

“It used to be that when you referred to the mobile worker you were talking about a person who works outside the office,” Busch tells Quartz. “Now you’re just as likely to be referring to someone that’s in the office environment, but they’re mobile because their technology has untethered them from their desk.”

Meanwhile, companies are becoming more conscious of the needs of different employees, according to Busch. Some people thrive on the energy of the open office (and it very likely is an open office) while more introverted people tend to suffer.

Both trends—the untethering and the desire to accommodate a range of work styles—point to a need for more variety in the space that companies offer. Desks are important, but so are more casual sitting areas where small groups can collaborate, as well as more private areas (the idea here being that there’s a space not only where people can go take a phone call, but one where someone who needs an hour of peace and quiet to finish something can find it).

And when there are space constraints, as is often the case, the need for gathering spots or private areas often comes at the cost of individual work stations, either in size, number, or personal ownership.

At the BBC headquarters in London, there are 3,500 desks for a staff of 5,600, spawning employee complaints about being able to find a place to work, and inspiring mockery in the organization’s own workplace comedy show.

The transition to unassigned desks appears to be going more smoothly in the human-resources division of Citigroup. Its workspace, in a Citi office complex in Long Island City, Queens, has 150 unassigned desks for 200 staff and has become a pilot in the company’s effort to “optimize the company’s workspace,”  according to a recent piece at the Harvard Business Review.

Previously, the group’s offices were underused—people were always out for one reason or another, be it vacation, illness, work travel, or because they had a flexible schedule.

It’s not anarchy at Citi. The office is loosely organized by function, there’s a locker room available to store stuff, and there are conference rooms and some shared private spaces available for meetings or phone calls. Despite the lack of seat assignments, Karyn Likerman, head of inclusion programs and work-life strategies, told HBR that she and her Citi colleagues tend to sit at the same desk most days, even though it’s not technically their space.