D.C. Schools Chancellor Kaya Henderson, prodded by the Washington Teachers’ Union, has relaxed teacher evaluation rules so that some veterans who receive two consecutive poor appraisals can keep their jobs.

Under original guidelines for the evaluation system known as IMPACT, teachers judged “minimally effective” two years in a row were subject to dismissal. About 550 received that rating last year, out of nearly 4,200 teachers citywide. Henderson said that she is unsure how many will be affected by the change but that it was likely to be no more than “a handful.”

Dismissal notices based on 2011 evaluations are expected to go out soon, possibly Friday.

The system, launched in fall 2009, has drawn national attention as the centerpiece of former chancellor Michelle A. Rhee’s efforts to upgrade teaching quality in the District. The union has been sharply critical of the initiative.

The shift could raise questions about the union’s influence with Mayor Vincent C. Gray (D), who was lobbied on the issue by union President Nathan Saunders. Gray received substantial support from organized labor in his 2010 campaign.

Neither Gray’s office nor De’Shawn Wright, the deputy mayor for education, returned calls for comment. Henderson said she met with Saunders to discuss easing the rule.

“I thought it was a reasonable request and one that we could accommodate, and we did,” Henderson said. “The mayor and I have never discussed it. In my conversations with the mayor, we don’t get into those kinds of micromanagement issues. The mayor trusts me to pursue the policies I think are right.”

Saunders praised Henderson on Thursday for taking steps to correct what he called the “unintended consequences” of IMPACT that have unfairly placed some good teachers at risk. He said that while Gray never agreed to intervene with Henderson, he was sympathetic.

“He always defers to Kaya, but when I remind him of how he got to be mayor and where he was on issues like this as [D.C. Council] chairman, he’s always thoughtful,” Saunders said.

IMPACT has drawn praise from some advocates for the rigor it has brought to teacher assessments. Traditionally, evaluations have been low-stakes exercises that award the overwhelming majority of educators with positive marks.

Under IMPACT, teachers are observed in their classrooms by principals and “master educators” five times during the school year.

They are assessed primarily for compliance with nine broad standards, including the ability to explain content clearly, to engage students with varied skill levels and to use skilled questioning to ensure that students understand the material.

For about 450 teachers whose classes take annual D.C. reading and math tests, half of their scores are based on whether student scores meet growth targets.

Last year, 126 teachers were fired for “ineffective” ratings, the lowest on the IMPACT scale.

Questions about the treatment of veteran teachers arose last month when the school system’s human capital chief, Jason Kamras, told principals that if they had second-year teachers with promise who seemed to be headed for a second consecutive poor evaluation, the principals could apply for exceptions to protect them from dismissal.

Kamras said the change was justified by research showing that new teachers can improve dramatically in their first few years.

But the exception drew a protest from Saunders, who said it discriminated against others who had been working under IMPACT for the past two years. The union and the District are engaged in a court fight over other aspects of IMPACT, and Saunders made clear that this issue could lead to another.

“There is no rational, non-discriminatory reason to offer and grant this exception to second-year teachers and not also to older, more experienced teachers,” he wrote to Henderson on June 16.

A series of conversations with Henderson followed. Kamras informed Saunders of the change last weekend. Saunders told union members in a robocall this week.

Henderson said it would be a mistake to conclude that she was backing away from the core goals of IMPACT.

“All through the IMPACT process there have been opportunities for us to correct any mistakes that we make or any issues that need clarifying,” she said. Allowing principals to advocate for teachers who show potential for improvement “doesn’t mean we’re backing away by any means.”