There’s some good news for the financially beleaguered Cambridge Health Alliance, but it’s far from bringing the health care system into the black.

The number of outpatient visits to Alliance doctors exceeded projections in April – the first month that has happened since the current fiscal year began last July 1, Chief Financial Officer Jill Batty told the finance committee of the board of trustees last week.

Outpatient visits edged past projections by a little less than 2 percent after accounting for a mistake that put about 2,000 visits in May figures instead of including them in the April report, officials said.

The number of primary care visits rose significantly because of a campaign to make it easier to get appointments, including improving efficiency and better managing referrals, spokesman David Cecere said. At the committee meeting, Chief Medical Officer Dr. Assaad Sayah described the effort as “hand-to-hand combat.” He was referring to “the constant attention being given to every variable and detail in areas including patient access, flow and physician productivity,” Cecere said.

In addition, the Alliance expects to get about $2.4 million from the state in increased Medicaid reimbursements, which was not included in the budget for this year, Batty said. And there will be “small amounts” of additional money from settlements with government and private insurers for the years from 2007 to 2012, Cecere said.

Until now, the news had been unrelentingly grim. The Alliance had expected to lose $19.3 million in this fiscal year, which ends June 30, but because of continuing shortfalls in volume, officials revised the forecast to a loss of $28.1 million.

The most recent performance report, for the 10 months ending April 20, shows continuing gaps. Hospital discharges, a measure of how many patients are admitted to the hospital, were off by 9.3 percent from expectations, and the Alliance lost $23.7 million for the 10 months. That’s far greater than the original projection, but less than the new forecast anticipated as of the end of April.

The Alliance includes the former Cambridge City Hospital, Somerville Hospital and Whidden Memorial Hospital in Everett, plus 15 primary care offices in Cambridge, Somerville, Everett, Revere and Malden. It serves more poor and uninsured patients than any other hospital in the state except Boston Medical Center, making it the second largest safety net hospital.

The Alliance has lost money on its health care operations since at least 2008. State aid for caring for the uninsured dropped after health care reform because state officials expected more people to get insured. Medicaid reimbursements traditionally fall short of hospital costs. For several years revenue from its Network Health business, an insurer that covers Medicaid patients, offset losses on medical operations, but the Alliance had to sell the insurer in 2012 because it didn’t have the required reserves.

Last year the Alliance and Beth Israel Deaconess Medical Center agreed to a clinical affiliation, helping both establish organizations that provide a complete spectrum of care from basic to advanced and charge insurers a set amount per patient. The Affordable Care Act gives advantages to such systems.

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