“Today, the administration is taking the next step in providing women across the nation with coverage of recommended preventive care at no cost, while respecting religious concerns,” Health and Human Services Secretary Kathleen Sebelius said in a press release. “We will continue to work with faith-based organizations, women’s organizations, insurers and others to achieve these goals.”

The proposed rule is aimed聽mainly at groups affiliated with churches, such as hospitals and educational institutions. It聽is unlikely to satisfy the concerns of private businesses, however, which聽have brought聽several dozen lawsuits聽against the health law’s contraceptive mandate saying it violates their religious beliefs.聽“The rights of family businesses like Hobby Lobby are still being violated,” said Kyle Duncan, general counsel of The Becket Fund for Religious Liberty, which represents several groups that have filed suit. Some of those聽lawsuits are expected to make their way to the U.S. Supreme Court.

Cardinal Timothy Dolan of New York, president of the U.S. Conference of Catholic Bishops,聽 that the organization welcomes “the opportunity to study the proposed regulations closely. We look forward to issuing a more detailed statement later.”聽 A similar was issued by the Catholic Health Association, which includes scores of hospitals and health groups affiliated with the Roman Catholic Church.

Here’s the way聽 would work:

It clarifies the definition of “religious employers” to follow that of Internal Revenue Service code, and to include all houses of worship and their affiliated organizations.

Religious organizations that self-insure, as well as student health plans, would let their third party administrator know that they object to聽providing contraceptive coverage on moral grounds. The administrator would then work with a health insurer to provide separate individual contraceptive coverage at no cost to the enrollees.聽 The cost would be “offset by adjustments in federally-facilitated exchange user fees that insurers pay,” according to the administration.

Nothing would change for a religious organization that offers a group plan: Under the compromise offered by the administration last February, the insurer would provide separate contraception coverage at no cost to participants. The administration argues that such services would be cost-neutral to insurers because they would result in fewer births.

Under the health law, employers who insure their workers are required to cover government-recommended preventive services without co-payments. In August 2011, the Obama administration said those would include contraceptive services, such as birth control pills, implants and sterilization procedures.

Religious organizations opposed to birth control sought to be exempt. The Obama administration initially gave them a one-year delay, until August of this year, to comply, while promising further compromise.

Ilyse Hogue, president of NARAL Pro-Choice America, praised the proposal, saying it聽would ensure that “most American women will get birth-control coverage without extra expense.”

But others skewered it.

“The contraception compromise is a compromise only from the perspective of the Obama administration,” said Benjamin Domenech, a research fellow at The Heartland Institute, a libertarian think tank in Chicago. “Nothing significant has changed. Religious employers will still be required by law to pay an insurance company that will provide sterilization, contraceptive, and abortion inducing drugs. That was true before this announcement, and it is still true today.”

Insurance consultant Robert Laszewski of Health Policy and Strategy Associates聽said the administration “way underestimated” the strong feelings about contraceptive services among聽some religious Americans. To fulfill its promise of no-cost contraceptive services, he said, the latest compromise transfers the costs of covering a relatively small number of women to the new health insurance marketplaces.

While that cost will eventually be passed onto consumers, he said, “we’re talking nickels and dimes here.聽The Obama administration is correctly assuming that the cost is going to be a rounding error.”

Nonetheless,聽that’s unlikely to satisfy religious employers for whom the issue聽was never about cost, but about religious principles, Laszewski said.

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