And it shall be known as the Peek-a-boo Building. That, at any rate, seems to be the consensus, in the initial print articles and on the Web, concerning the building that Rem Koolhaas has just designed at 23 E. 22nd St., renderings for which were officially made public last week. The reason for the odd moniker is the way this 22-story structure, configured in a stepped succession of cantilevered floor plates, seems to peer out sneakily from behind the back of the much taller One Madison Square, directly to its north on 23rd Street. That fine building, now essentially complete, comes from the same developers, Ira Shapiro and Marc Jacobs of Slazer Enterprises, and will apparently share a lobby with its new neighbor.

Mr. Koolhaas, a native of Holland, has designed a number of projects for New York City, few of which — the exceptions being his Prada store in SoHo and Second Stage Theatre, a redesigned space on West 43rd Street — have come to anything. Assuming that he has more luck with this latest project, for which ground has already been broken and which is scheduled for completion in 2010, it will be his first residential tower anywhere.

As Julie Iovine pointed out recently in the New York Times, the new project seems in part to be inspired by Mr. Koolhaas’s book “Delirious New York” (Monacelli Press), published in 1978. In that work, the author delighted in the clamorous, calamitous energy and diversity of Manhattan, especially during its pre-war building boom in the 1920s and ’30s. Those were the years, prior to the introduction of the International style, that brought us such iconic skyscrapers as the Chrysler, Squibb, and Empire State buildings, as well as Rockefeller Center. The step-wise progression of the floor plates on 22nd Street can thus read as a tribute to, as well as a benign parody of, those curiously zigguratted skyscrapers that arose in response to the building code of 1916.

To most viewers, however, the new Koolhaas design will seem to take its cue from deconstructivism, which is surely an influence, not only in its overall conception, which flies in the face of the stiff rectilinearity of the International style, but also in its woozy, off-kilter stretching of Modernist notions of modular design at each level.

The building rises as a setback over an eight-story base, the first five stories consisting of a curtain wall. To the east, the façade takes the form of five cubes that, perhaps intentionally, recall the façade of One Madison Park. To the west, the renderings promise a narrow, five-story atrium. Above the fifth floor, however, the glass yields to concrete and steel cladding and the windows assume different sizes and shapes depending upon the height of the ceiling on any given floor. Directly above the curtain wall of the base, the windows take on the form of elongated rectangles, with relatively little infill between them. One level up, the infill becomes more pronounced around the rectangular windows, but is most evident around the squatter, squarer window-work in the third elevation. Finally, at the summit of the building, glass comes into its own again, virtually to the elimination of infill.

The very premise of the deconstructivism associated with Rem Koolhaas is naturally one that embraces syncopation and irregularity, such as are fully borne out in this latest project. That quality has always been visible in this architect’s finished works, whether in his early Euralille complex in northern France, his Prada store in SoHo, or his student center at the Illinois Institute of Technology in Chicago. But even when it serves as an obvious and intentional illustration of the principles of the Deconstructivist style, there has always been an ad hoc quality to these designs that, to some of us, feels lacking in method. It is one thing to deconstruct, and another thing to seem arbitrary. Whether Mr. Koolhaas can overcome that impression on 22nd Street remains to be seen.

What will likely impress more pedestrians, however, is the curious game that his pale, off-white building will play against its dark and austerely rectilinear neighbor to the north, the 50-story One Madison Square. Mr. Koolhaas’s contribution will be Lou Costello or Jerry Lewis to the Bud Abbott/Dean Martin of its neighbor. Peeking out from behind the back of the taller building, it will deliver the impish and subversive laugh lines, while the taller building, the grown-up straight man in the equation, will preserve its unflappable rectilinear integrity. That should be interesting to see.