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The Atlanta Symphony Orchestra Players’ Association made a counterproposal to administrative leaders of the ASO and Woodruff Arts Center on Monday that draws the two sides closer to an agreement as the musician lockout enters its eighth week.

The Players’ Association (ASOPA) made compromises on the matter of the size of the orchestra, which was reduced from 95 to 88 full-time musicians in the 2012 collective bargaining agreement and which management proposed last week should shrink to the 76 players who remain.

ASOPA proposes starting this delayed season with its count of 77 remaining musicians (after defections, retirements and deaths), with an uncontracted expectation of “best efforts” by management to build the “complement” to 81 by the end of 2015-16.

Management would then be contracturally obligated to build to a minimum of 84 by the end of the 2016-17 season and a minimum of 88 by the end of 2017-18, “with best efforts to restore complement to 90 musicians,” according to the ASOPA proposal.

The last offer from leadership of the ASO and its parent nonprofit the Woodruff (WAC), after three days of federally mediated talks last week, guaranteed the 76 jobs over the four years, with no further downsizing.

Management said in its proposal that it would launch a major fund-raising campaign where proceeds exclusively would endow musician chairs. Its pledge — though it was not promised as part of the contract — was that it would build the size of the orchestra “over time as we can afford to do so — up to 90 players,” ASO/Woodruff lead negotiator J. Thomas Kilpatrick wrote.

The size of the complement has emerged as the biggest point of division since Sept. 7, when management locked out the musicians for the second time in two years.

“We are allowing the WAC/ASO almost three years to get to a minimum guaranteed complement of 84 musicians at the end of year three by using best efforts to hire musicians until then,” ASOPA vice president Daniel Laufer told The Atlanta Journal-Constitution on Monday. “That is enormous flexibility on our behalf even though we have extreme concerns that we can function without an immediate larger complement.”

An ASO/Woodruff spokesman said its negotiating team was meeting Monday afternoon to review and evaluate the musicians’ proposal, but that a decision probably would not be made public immediately.

Even after the 2012 cut from 95 to 88 full-time musicians, ASO and Woodruff leaders said they were left with no choice but to seek the additional reduction this time as a strategy to help halt 12 years of orchestra deficits, including $2 million in fiscal 2014.

The musicians have said repeatedly throughout negotiations that further cuts to their ranks would turn the Grammy-winning orchestra into a minor-league ensemble. ASO music director Robert Spano and principal guest conductor Donald Runnicles loudly backed them on that point, even though musical leaders are typically mute during labor disputes.

By comparison, the Chicago Symphony Orchestra, currently amid a European tour with the ASO's Christina Smith as guest principal flutist, has a contracted size of 106 full-time players. The Cleveland Orchestra has 104.

The Players’ Association’s Monday counterproposal also calls for raises of 1 percent in 2014-15 and 1.5 percent in years two through four.

ASO/Woodruff leaders had offered a graduated 4.5 percent increase over the same period.

The two sides agreed last week on the third major issue, health care coverage, with musicians set to pay $20 a week for the four years in a high-deductible plan.