The Bloomberg administration has long touted the small high schools it created as outperforming large schools closed to make way for them. But a new report finds, for the second time, that the schools also post higher graduation rates than other city schools that stayed open.

Being randomly selected to attend small high schools opened under the Bloomberg administration made students significantly more likely to graduate, even as the schools got older, according to the report, conducted by researchers at the nonprofit firm MDRC.

The researchers updated a 2010 study that examined “small schools of choice” that opened between 2002 and 2008 and did not select students based on their academic performance. Of the 123 schools that fit that bill, 105 had so many applicants that the schools selected among them randomly, through a lottery.

The lottery process enabled the researchers to compare what happened to two groups of students that started out statistically identical: those who were admitted to the small schools and those who lost the lotteries and wound up in older, larger schools. That type of comparison is considered the “gold standard” in education research.

The original study found that the small high schools had positive effects on their students — but it looked only at the schools’ very first enrollees. The new report looks at those students in the fifth year after they enrolled and also at the second set of students who enrolled at the schools.

It finds that the higher graduation rate — 67.9 percent, compared to 59.3 percent for students who were not admitted — continued for the second group of students who enrolled and cut across all groups of students, regardless of their race, gender, family income, or academic skills upon enrollment. Students at the small schools were also more likely to meet the state’s college readiness standards in English, though not in math.

“Small schools for a variety of reasons, I always felt, were going to succeed in certain ways,” said Richard Kahan, the head of Urban Assembly, a nonprofit that started a handful of schools included in the study. “But I would not have predicted the impact.”

Together, the 105 small schools served more than 20,000 students when studied and will ultimately enroll about 45,000 students every year — a number, the report notes, that rivals the high school enrollment of all but a handful of school districts across the country.

The report is part of a series funded by the Gates Foundation, which put $150 into the city’s small schools before ending its small-schools giving in 2008, citing lackluster college readiness rates. The new report does not track students into college to see whether they succeeded or even remained enrolled. But it does find that the graduation rate boost for the first two cohorts of students in the city’s small schools was driven largely by receipt of Regents diplomas, considered more rigorous than the local diploma option that is being phased out.

The report does not conclude that it was size alone that made a difference for the small schools. Instead, it suggests, the schools shared specific design elements that might have driven their impact on students.

“New York City’s [small schools] were developed through a demanding proposal process that was designed to ensure specified conditions and to stimulate innovative ideas from a range of stakeholders and institutions,” the report notes.

That process is no longer in use, although the city’s current new schools proposal process shares some characteristics and approaches.

Robert Hughes, the CEO of New Visions, a group that started about 60 of the schools in the study and now works to support a range of schools, said some efforts were underway to identify just what it was that led to the higher graduation rates at the small schools.

“We’re constantly trying to take what we’ve learned in these schools and push it out and conversely try to learn from all schools,” Hughes said.

MDRC will continue to produce reports chronicling the small schools’ impact and will turn its attention next to looking for distinctions among the small schools, according to the report. One open question is whether a change in city policy, to require the schools to admit students with special needs and English language learners from the start, affected the schools’ impact on students. The schools were not required to admit those students to the cohorts the new report examined.

MDRC’s complete report is below.