The Board of Education approved merit-based raises averaging 3.5 percent Tuesday for nearly two dozen senior Department of Education executives.

The board previously rejected a proposal from schools Superintendent Kathryn Matayoshi seeking across-the-board 4.5 percent raises for 23 of her top executives including the department’s deputy superintendent, six assistant superintendents and 15 complex-area superintendents.

After some BOE members questioned the approach of across-the-board increases, the department came up with a revised recommendation that ties individual raises to performance:

>> Two executives rated as “fully meets expectations” will receive a 2.4 percent raise based on cost-of-living increases.

>> Sixteen executives rated as “exceeds expectations” will receive a 3.4 percent adjustment.

>> Five executives rated as “exceptional” will receive a 4.15 percent increase.

The Board of Education is authorized under state law to set the salaries for these positions, without exceeding that of the superintendent, who earns $200,000. Matayoshi, who received an “exceeds expectations” rating from the board in September, is not included in the raises.

“We’re happy that they’re getting an increase because I think it’s well deserved,” Matayoshi said after the board vote. “It recognizes the hard work and achievements of the complex-area superintendents and assistant superintendents. It was agreed that if they’re performing their job well, they should at least get a cost-of-living increase, which is that first level, and then after that, if you’re at the next level, you get a little more, and if you’re at the top level, then you get a little more.”

Matayoshi said the average raise amounts to 3.5 percent, with an average dollar increase of $4,839. Altogether the raises will cost $110,675 — about $33,000 less than the original across-the-board proposal would have cost — and be effective retroactive to July 1.

With the increases added, the deputy and assistant superintendents will be earning salaries ranging from $143,023 to $166,681. The deputy superintendent acts as chief academic officer for the department while the assistant superintendents run central offices that oversee human resources, fiscal services, information technology, school facilities and support services, curriculum and instruction, and strategy and innovation.

Complex-area superintendents, meanwhile, oversee the 15 school districts statewide. The department’s complex-area superintendents will begin earning salaries ranging from $129,250 to $157,676 after the raises are added.

By comparison, salaries for school principals, who are unionized, range from $102,000 to $185,400, according to the DOE. Officials have said that 13 principals earn more than the deputy superintendent, and more than 20 principals make more than the senior assistant superintendent.