A much-touted plan that city officials said would fully insulate public schools from budget cuts this school year appears to have fallen short, especially for some of the neediest schools.

Mayor Bloomberg proposed a budget last spring that would have sent the city Department of Education $428 million less than was scheduled for this school year, but the blow was softened by cuts from the department’s central office and an influx of $129 million from the City Council speaker, Christine Quinn.

Officials said the influx would ensure that all New York City schools would open this fall with at least the same amount of funding as they had when the school year ended in June.

Some principals looking at their budgets have seen a less perfect picture.

The snag is that while some schools saw their budget gaps closed with an influx of regular city dollars, which are unrestricted and thus can be spent anywhere, others received mainly restricted dollars that can be spent only on certain programs. The restricted dollars also have no matching program to cover the cost of health and retirement benefits for newly hired teachers, as city dollars do.

That means that if principals’ budgets were closed mainly through restricted funds, and if the principal wanted to use the new funds to hire a new teacher, the dollars would have to stretch further — covering not just the teacher’s salary but also the 39% of the salary estimated to be the cost of benefits.

School officials said the education department tried to help principals avoid paying those extra benefits costs, and in some cases even offered extra funds to help them cover costs.

The officials pointed out that principals could rearrange which dollars they spent on which programs, shifting other city dollars to pay for teachers and using restricted dollars to pay for other programs. The main pot of restricted funds used to close the budget gaps is the Contracts for Excellence dollars, a set of state money that can only be spent on six specific programs and that only goes to schools with needy students.

“Budget support teams at the Integrated Service Centers helped principals optimize their use of these different funding sources,” a spokesman for the department, Andrew Jacob, said. “Where we determined that a school would have difficulty paying fringe costs associated with Contracts for Excellence spending, we provided them with additional funding.”

Principals who spoke to The New York Sun on condition of anonymity said they did not think their colleagues were all aware of the extra funding available to cover benefits.

They also pointed out that moving funds around is not as easy as it might look; although city funds can be spent anywhere, principals have to prove that they are spending restricted dollars on the authorized programs.

Contracts for Excellence funds are also banned, for the most part, from paying for existing programs; they can go only toward new programs — a restriction that principals said makes hiring a new teacher an ideal option.

School allocation memos suggest that, in bringing school budgets to a net zero change from the end of the last school year, the city first distributed a pot of $63 million in Contracts dollars.

Those dollars are required to go primarily to schools with needy children — poor students, students with disabilities, students not meeting academic standards, and non-native English speakers.

Schools such as Lehman High School in the Bronx, where about 60% of students are eligible for free lunch and 55% are recent immigrants, received more than $577,000 in the restricted Contracts funds.

After allocating all the Contracts funds, the city appears to have added city tax-levied dollars to those schools still facing cuts. The unrestricted city dollars went primarily to schools with more affluent and high-achieving students.

The top-rated exam high school in the city, Stuyvesant High School in Lower Manhattan, got $955,000 in city funds.

Brooklyn Technical High School in Fort Greene, an exam school ranked just behind Stuyvesant, received more than $1 million in city funds.

Neither school received Contracts for Excellence money.

While Stuyvesant’s $955,000 could be spent in any way the principal chose, Lehman’s $577,000 was restricted.

Had both schools chosen to use the money to hire new teachers, Stuyvesant’s dollars would have gone further, thanks to the matching grants covering health and retirement benefits at no expense to the school.

The city Department of Education had heavily protested the restrictions on the $63 million pot, pleading with the state to let it send those dollars equally to all schools.

A school official who is a budget expert last week said that the department maintains its opposition to the restrictions. The official asked not to be identified.

A spokesman for the council, Jamie McShane, said, “The council’s goal was to ensure that no city school suffered a budget reduction. The council remains confident that goal was accomplished.”