Open enrollment - but with a few strings attached - may return to Salt Lake's three high schools in fall 1992.

The Salt Lake Board of Education on Tuesday night asked Superintendent John W. Bennion and the Salt Lake District staff to draft a proposal for open high school enrollment as a way to deal with the lopsided East-Highland enrollment.After a far-ranging discussion looking at various ways to increase East's dwindling student body, the school board seemed to like best the suggestion of board member Stephen G. Boyden: The city's three high schools would maintain their current boundaries, and students living within a particular school's boundary would be given priority for attendance there.

Students from other areas then would be free to transfer to the school of their choice on a space-available basis. However, to prevent overcrowding each school would have an enrollment cap.

Bennion said he would draw up a tentative proposal along those lines. He also will examine the possibility of other guidelines for minority enrollment and academic balance.

Board member Diane Barlow suggested that Bennion work individually with board members on the tentative proposal before bringing it back to the board for a decision.

The move toward open enrollment - an issue that the board has revisited many times since redrawing high school boundaries three years ago - was prompted by East parents upset over the school's dwindling enrollment.

One criterion used in the old boundary adjustments was that high school enrollments should be balanced as closely as possible with no more than a 200-student difference between schools. Other criteria included a balance of test scores and minority populations.

Highland has about 500 more students than East. In the past two years, East has lost 10 teachers because of dwindling enrollment and is projected to lose one or two more next fall.

With only a few exceptions, the board has prevented high school transfers since 1988 as a way to stabilize the boundaries. However, members said Tuesday night that by fall '92 the first generation of students under the new boundaries will have graduated from high school, so it may be time to relax the restrictions a little.

Two weeks ago, East parents demanded the board follow the old boundary criteria or abandon them. They pushed for redrawing boundaries again or opening enrollment for next fall.

A Highland spokeswoman opposed what she called "boundary tinkering" Tuesday night. Barbara Owen of the Highland Community Council, an organization of parents, teachers and administrators, said the school needs stability, not a constant shuffling of boundaries.

Another boundary change "would send the message that this type of disruption is accepted and expected for the future," she said.

The city's high schools need to work together as a group, not be constantly pitted against each other in a boundary battle, she said.