City Hall will bend its development rules to accommodate a new affordable housing project in the Pinckney neighborhood.

The Lawrence City Commission on Tuesday voted to share the cost of improving streets for the six-house project at Third and Alabama streets, even though city policies call for those costs to be entirely shouldered by the developer.

“I think it’s a fair result,” Commissioner David Schauner said. “I think it serves a good public purpose. And frankly, I think it’s the right thing to do.”

Tenants to Homeowners is sponsoring the construction of the six new houses, which will be made available to low-income working families, single parents and Lawrence residents with disabilities. After subsidies, the houses will cost their new owners a maximum of $60,000.

Under the city’s development rules, the owners of those new houses also should help pay to upgrade both Third and Alabama streets. But officials with Tenants to Homeowners said those rules could tack up to $20,000 onto the cost of each house, putting the homes out of financial reach of the people they were intended to serve.

“The people we want to get into these homes … don’t have the option of increasing their incomes,” said Alan Bowes, Tenants to Homeowners’ director. Requiring them to pay for street construction “will eliminate some of those people.”

Commissioners settled on a 75-25 percent split for the cost of Third Street, and said Alabama Street improvements were not needed. That would put the additional cost for the new houses at roughly $3,000 apiece.

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Commissioners rejected calls to pay the entire cost of Third Street.

“I’d like to do anything we can to make this project happen,” Commissioner Boog Highberger said. “We have to balance it against the needs of the rest of the city.”