New York City Mayor Bill de Blasio’s inaugural State of the City address contained a little bit of music to my ears. To address the question of housing affordability in America’s largest city, he said, “we want to work with the real estate industry to build”—not as a matter of centrist or pro-business pablum, but as a simple necessity. “We MUST build more to achieve our vision,” he said, with all-caps right there in the transcript.

The idea of a de Blasio construction boom has been circulating on the Web for a while, based in part on some development-friendly staffers and in part on his record of support for the Atlantic Yards project, the controversial real estate development in Brooklyn that tended to pit a business/labor alliance against lefty anti-development activists. But despite the emphatic “MUST,” the substantive construction agenda for New York City is rather paltry. The most striking quasi-concrete idea offered was a “pledge to preserve or construct nearly 200,000 units of affordable housing.” Read swiftly, that sounds like a lot. But the allusion to preservation renders it almost meaningless. A city with 3.3 million housing units—most of them extremely expensive by national standards—with a growing population, and aspirations to continue becoming more desirable through job creation, falling crime, and better schools can’t simply slow the rate at which subsidized dwellings vanish. As de Blasio himself said, it actually needs more places for people to live.

In particular, it’s worth looking at the construction of market-rate and affordable housing as less of an either-or. Earlier in the speech, de Blasio spoke of “requiring developers to build affordable homes for everyday people rather than simply multimillion dollar condos.” This is a reference to the idea of inclusionary zoning rules. For example, these might require that for every four market-rate units constructed, a developer must sell (or rent) one unit at a discount price. It’s a kind of backdoor tax on high-end development to generate some subsidized housing.

But in a city with a median household income just below $52,000, there’s actually a broad middle ground between a multimillion-dollar condo and a home that would be affordable to the bottom one-third or one-half of the population. The key issue for New York City is that the supply of new building permits is tiny relative to the demand for new housing, leaving even reasonably prosperous New Yorkers priced out of many neighborhoods if they didn’t buy early enough. That’s why the raw quantity of market-rate housing makes a difference. Since developers are only allowed to build a handful of market-rate units, then they really will target the ultra-luxury segment. But the fact is, there are only so many billionaires out there ready to buy a home or pied-a-terre. Given a less constrained zoning code and broad authorization to build more units, you soon run out of multimillion dollar condos to sell. Soon enough, developers are unloading brand new construction for a mere $1 million, or even less. The median value of the existing stock of owner-occupied houses in Manhattan is pricey at $827,000, but still a good deal cheaper than the super-expensive projects that have made waves recently.

Such homes would still be out of reach for a great many people. But putting a large number of them on the market would reduce the trend toward gentrification and replace it with filtering. In other words, affluent people would buy up fewer poor people’s homes in marginal neighborhoods; instead they would buy more shiny new construction. As it aged, it would become more affordable and the less well heeled might move in. That kind of broad supply-size reform isn’t a panacea for housing affordability, especially for the truly poor. But it’s a powerful complement to inclusionary zoning, because the success of IZ policies in producing discount housing is driven by how much market-rate construction is allowed.

Restrictions on housing supply sometimes enter through the backdoor. For example, New York could increase construction and affordability by scrapping the mandatory parking minimums that plague New York’s outer boroughs. Regulatory parking minimums are never a good idea. But they’re especially egregious in a place like New York, which combines an acute affordable housing crisis with a world-class mass transit system. In effect, low-income residents of Brooklyn, Queens, and the Bronx are being taxed to provide discount parking to the boroughs’ more affluent residents.

But more broadly, de Blasio and his team ought to print out a nice big zoning map of the city and go over it inch by inch. Find the residential neighborhoods that are currently built out to capacity, and rezone to allow for more housing. Find the commercial- or industrial-zoned areas that are currently under-built, and rezone to allow for more housing. Neighborhoods vary, so in some places tough inclusionary zoning rules will make upzoning an easier lift. In others, it would make it harder. In either case, it’d be worth proceeding with whichever path is more feasible. Realistically, even a market-rate-only upzoning still reduces citywide housing pressures. Even better, it generates tax revenue and jobs (which themselves generate tax revenue) that can finance additional housing subsidies.

New York’s new mayor has given his housing team a May 1 deadline to outline a plan to meet his goals. The 200,000 “preserve or construct” target could be hit through various means. But to achieve the spirit of de Blasio’s proposal they’ll need to think bigger. When it comes to new housing, more is more—and New York City’s aim should be to get us much of it as possible.