The difficulty of using a qualitative measure weighs on city officials’ minds as they prepare the outlines of a new testing contract that will go out for competitive bidding to the nation’s testing publishers in the fall. Cost is another key factor.

Because the city wants to keep the testing process free, the tests are administered by teachers, a much cheaper method than the psychologist-administered intelligence tests of the sort used for private schools, which cost hundreds of dollars per student.

Early testing is something else the city wants to maintain. A number of the city’s most treasured schools for the gifted — like Anderson, NEST+m and Lower Lab — begin in kindergarten, and the city said it did not want to tinker with those programs, which are popular with middle-class parents. Waiting until later grades to start gifted classes and schools, city officials said, would also present a daunting logistical challenge, with children moving from school to school in the middle of their elementary years.

This despite the fact that many experts say preschool intelligence testing is less accurate than testing once school is under way, in part due to the strong impact of nurture on the early acquisition of skills. On the other hand, the city’s lower-than-average cut-off scores for gifted programs — the equivalent of 120 I.Q., or the 90th national percentile, rather than the 130 I.Q. used by most gifted programs — helps ameliorate this variability, some experts said. (The city tried using a higher standard, but amended it in 2008 after fewer students qualified, causing an outcry among parents in some districts.)

City officials said they hoped that advances in psychometrics since the last testing contract could lead to a fairer test.

And in fact, there have been advances in the last decade, particularly in two aspects of testing — new nonverbal aptitude tests, in which test examiners use pantomime instead of verbal directions to take students through the patterns and logic questions on the exam; and in item-response theory, which determines test validity question by question, instead of for the test as a whole, testing experts said.

But even with the advances, staying with a testing-only model would be unlikely to correct for the problem of low minority representation in the gifted program, some experts said, drawing on evidence from around the country. Currently 44 percent of children in New York City’s gifted programs are white, compared with 15 percent in the overall school population.