After David Adjaye, a London-based architect with a busy international practice, was hired to design two libraries for the D.C. Public Library system in 2008, he said in an interview that public buildings “should offer places for people to see beautiful things, be inspired, just exist, engage or just do their own thing.” It sounded, perhaps, like the usual, feel-good patter that architects use to describe inchoate plans. But it turns out he meant exactly what he said, and now that both buildings are open, it’s clear that’s exactly what he has provided.

In the past two weeks, the Adjaye­-designed branches have begun to serve their neighborhoods. The Bellevue branch in Southwest Washington, which opened June 13, comes bursting out of a hillside, with arms and pods energetically reaching out into what is an underserved and economically depressed neighborhood. The Francis A. Gregory branch in Southeast, which opened June 19, is more serene, a quiet, shining pavilion of mirror and glass set into a dense, unruly bit of urban forest. But both are distinguished by interior spaces that are inviting, that make one want to sit and reflect and read and “just exist.”

The wisdom of having hired Adjaye is abundantly clear. Built on a tight budget (they cost slightly more than $13 million each), with a strict and demanding program, the libraries are nevertheless vibrant, strong and practical buildings. And although one might not immediately guess that they are the work of one architect — a young, international star who is also designing the Smithsonian’s National Museum of African American History and Culture — it’s clear that the same sensibility is at work. They express a similar, well-channeled exuberance, a playfulness that is never merely arbitrary, and a deep sense of respect for what the building should do and for whom it does that work.

The Bellevue branch, at 115 Atlantic St. SW, has consistently been the more controversial of the projects, and it is also the more daring design. When renderings were released to the public, they presented something radically different from the staid and dilapidated 1959 building that was being replaced. The new structure was made of concrete, lined with wooden slats, with large rectangular windows that wrapped around the corners of its geometrical forms. Some neighbors objected, saying it would be out of place on streets filled with small single-family, mostly brick homes. Later, a typical Washington fracas would erupt about the name of the library. It is now officially known as the William O. Lockridge/Bellevue Library, by fiat of the mayor and the D.C. Council, even though Lockridge, a neighborhood activist, opposed the building before he died last year.

All of that deserves to be forgotten. The Bellevue branch is a virtuoso work, proof of what can be accomplished if an architect is attentive to past ideas but not enthralled with them. Adjaye has set the building atop stout pilotis, or piers, that raise the building off the ground in a way that recalls the work of Le Corbusier. This gesture fell out of fashion, and its unthinking use in too many bad buildings of the past century makes it deservedly controversial. Very often, the space created under a building on pilotis is unwelcoming, and the pillars don’t seem like supports but like poor, exhausted Atlas bearing a crushing weight on his shoulders.

But given the sharp slope of the plot on which the library sits, the pilotis are the right choice. They lift the library up, creating a covered plaza that reaches out to the street with far more appeal than a slope of empty grass. It’s a small building, so the space underneath isn’t huge. It feels cool and cozy rather than arid or inhuman. And the boost these pillars give to the library’s second and third floors helps integrate the building into the hillside and breathe life and air into its various parts.

Adjaye acknowledges some people will see the library as filled with references to the 1960s, with its raw concrete, perhaps even brutalism, which was not his intention. Very sensibly, he argues that he is interested only in appropriating the best features of the architecture of this era, its formal freedom and un-self-conscious adaptability to program and setting.

Only if you look closely at some of the interior elements of the Bellevue branch — the intimacy of its children’s room, the long, stylish staircase that connects the second and third floors, and its enticing invitations to reflection and people watching — do you see its family resemblance to the Francis A. Gregory branch. Clad in diamond-shaped glass and mirrored panels, the Francis A. Gregory site is formally more simple, a rectangular box with a large, louvered canopy atop. If the Bellevue branch seems to reach out of a hillside into the city, the Francis Gregory branch, at 3660 Alabama Ave. SE, looks as if it has just materialized at the edge of dark forest. Walk around the library, to the grass-covered terrace at the back, and you feel as if you are in one of the city’s finest embassies, facing Rock Creek Park or on the porch of some billionaire’s posh home in Potomac.

If the basic shape is a plain rectangle, the diamond-shaped windows enliven it to the point of pure delight. No two are quite the same. The diamonds are pulled and stretched to give the facade energy, and from the inside, their vertical elongation at the corners makes the building seem to soar. The windows wrap around an interior core, where meeting rooms, office, bathrooms, reading and work spaces are arrayed. But one never feels far from the forest, and a reading space for children, with window nooks that invite kids to curl up and read as if nestled in a treehouse, will make adults pine for the undistracted, lost-in-fantasy, total-immersion reading of youth.

In short, these are spectacular libraries, and they deserve to be on any serious architectural tour of the District. That they are in neighborhoods that are not on the tourist map and that are relatively distressed economically should make them objects of emulation for other cities. This is service and good governance, and a source of hope for a society that too often sees economic inequity as an inevitable.

The choice of Adjaye came, in part, after Chief Librarian Ginnie Cooper visited one of Adjaye’s Idea Stores in London. The Idea Stores are also libraries, but rebranded for a new age of media and the Internet.

After seeing Adjaye’s libraries here, and several other almost as good library projects that have emerged as part of a renovation program that has spent $178 million since 2007, it’s a relief that they haven’t been branded in any way. They are updated and modern, and serve their patron’s needs in a way that goes well beyond loaning books, but they are still simply libraries, humble, useful, essential elements of the cultural infrastructure. And they are simply good buildings, and that has become the library’s brand. If you pass by a bit of architecture in the District that seems uncommonly interesting and effective, the chances are it’s a library. Quality needs no gimmicks.