The recent program my colleagues and I developed which sets aside more than one third of the seats at a "gentrifying" elementary school for immigrant and poor children was borne from unique circumstances. Still, I believe it's worth understanding how and what we did and perhaps emulating it when the conditions are right in other parts of the city.

By all accounts, this was the first time under the Bloomberg administration that the Department of Education agreed to implement a diversity program. And it started with the real estate, like so many New York stories.

Once upon a time, the School Construction Authority claimed there was no available property in District 15 - which includes Cobble Hill, Carroll Gardens, Red Hook, Gowanus, most of Park Slope, Windsor Terrace and Sunset Park - to construct a school even though there was an extraordinary need for several - especially in Sunset Park. Also, the city's capital plan for years allocated funds for such construction in our district.

Meanwhile, even though the adjoining District 13 - which includes Brooklyn Heights, the northern end of Park Slope, Fort Greene, Prospect Heights, Clinton Hill and part of Bedford-Stuyvesant - had no capital funds allocated for them, the SCA had found space to replace and expand the existing P.S. 133 school building. From this, a kind of marriage was made wherein District 15 would be allocated the additional capacity created in the new building while District 13 would keep its existing capacity and overall administrative control of the school.

The mechanism for admissions to the new school building, however, remained an open question.

At roughly the same time, additional capacity became available to District 15 when the D.O.E. procured a long-term lease on the former parochial school building which was temporarily housing P.S. 133 while its new building was under construction. In its wisdom, the department determined that the space on the eastern fringe of Park Slope could best be used to relieve the severe overcrowding in the popular nearby P.S. 321. Because the last real power Community Education Councils retain under mayoral control is the authority to approve or disapprove re-zonings, that decison had the unintended consequence of affording the councils with the leverage they needed.

Initially, the D.O.E. planned for the new P.S. 133 to become a "school of choice" in both Districts, meaning it proposed simply "de-zoning" P.S. 133 and incorporating its existing zone into the northern Park Slope P.S. 282 school without any provision for encouraging or maintaining diversity in either school.

The alternative of rejecting the "de-zoning" of P.S. 133 was not that much better. It was universally recognized that the District 13 allocation was far larger than the number of children residing in the existing catchment area. Thus, the remaining District vacancies would, in effect, be filled at the principal's discretion and, no matter how well intentioned she undoubtedly is, there would be great incentive for her to give preference to well-resourced and engaged parents.

It was, in large part, with that in mind that CEC-13 came to enthusiastically support a "targeted admissions" program that gave preference to low-income children (who are more concentrated on the eastern part of District 13).

CEC-15 faced similar issues with respect to those schools near the new P.S. 133 but, most importantly, the D.O.E.'s proposal failed to adequately address the actual capacity needs of District 15.

As it happens, there is little need in the immediate area for the added capacity that the new P.S.133 building will provide. At the same time, the D.O.E. has been unable to ameliorate the egregious overcrowding in the largely immigrant Sunset Park portion of our District. Because CEC members wanted to encourage parents from that neighborhood to come to P.S. 133, the council demanded that there be a preference given to English Language Learners, or ELLs, in any lottery for admission.

Out of the discussions and arguments consensus was reached between the members of both districts' councils for the targeted admissions solution

Now, we had to wrest an agreement from D.O.E. officials.

When the members of CEC-15 received the Park Slope rezoning proposal, we made it transparently clear to the Director of Planning that we would not approve the proposed rezoning of P.S. 321 (no matter how meritorious) absent a satisfactory resolution of the P.S. 133 admissions demand. This put the ball in the D.O.E.'s court, and it knew five things.

First, both CECs were united in their demands. Second, the law required approval from us for any District 15 rezoning to happen. Third, we could absolutely deliver on our threat. Fourth, even though the highly regarded principal of P.S. 321 had come to support the rezoning, it would be politically safe for us to reject the contentious D.O.E. proposal. Last, but not least, a majority of CEC-15 could be brought around to approve an appropriate rezoning.

And thus the D.O.E. was obliged to bargain in good faith, as were we, and an outcome was reached that was better than either side's original proposal.

The resulting "algorithm" will be applied in separate lotteries for each District and will work as follows:

First, there is a 35 percent set aside for ELLs and students who receive free and reduced price lunch. Within that set aside, ELL students will have absolute priority. Any remaining children within that pool will be placed in the general pool where each applicant will have an equal chance at admission. If the set aside is not filled, then those remaining seats would be put into the general pool.

Now let's apply that "algorithm" to the plausible scenario where the number of "advantaged" applicants outnumber the "disadvantaged" by two to one in a pool of 90 seats with 180 applicants (and using a one-third set aside). In that case, the "disadvantaged" would get the 30 set aside seats and the remaining 30 "disadvantaged" would be placed in the "general" pool along with the 120 "advantaged" applicants for the 60 remaining seats. Assuming a random selection, each of the 150 children would have a 40 percent chance of "winning the lottery." Thus, an additional 12 "disadvantaged" children would be admitted and 48 "advantaged" would be added.

As described above, the odds for each "disadvantaged" applicant rises to 70 percent while that for each "advantaged" applicant drops to 40 percent. Yet, in that circumstance, the "advantaged" admissions would still outnumber the disadvantaged by 48 to 42 instead of the 60-30 breakdown that would result without targeted admissions. That would be precisely the kind of outcome we fully intended.

While the D.O.E. may claim this is not a precedent, I believe it is. At the same time, the particulars of our admissions plan reflect the unique circumstances facing our two Brooklyn Districts. As such, it was never anticipated by anyone as a one size fits all solution. Still, our experience provides an example and a framework of what can be done when the D.O.E. is obliged to listen to and negotiate with Community Education Councils on an equal footing.

This is an edited version of a column first published on the blog NYC Public School Parents.