Still, requiring doctors who perform abortions to have admitting privileges at a local hospital would most likely identify unqualified doctors, the law’s proponents say. The process is extensive. Doctors’ credentials are vetted rigorously and their hospital records are reviewed regularly. If Dr. Gosnell had begun such a process, it would have quickly revealed that he was not board-certified in obstetrics or gynecology.

Another benefit, proponents say, is continuity of patient care. Doctors who perform abortions, particularly in rural areas, may travel among facilities, rather than have a full-time position at one clinic, said Dr. Ingrid P. Skop, an obstetrician-gynecologist in San Antonio, who does not perform abortions. “So it’s virtually unheard-of that any of them would be able to take care of a complication,” said Dr. Skop, who testified at legislative hearings in favor of the law. “If I have a patient with a complication, I’d want to take care of her in the hospital.”

Also, physicians with hospital privileges, she said, are regularly monitored for the complication rates of patients they admit to the hospital.

But there are many obstacles not only to gaining admitting privileges, but also to maintaining them.

Physicians are required to live and work near the hospital where they have privileges, so they can take on-call shifts and attend administrative meetings. Because doctors willing to perform abortions are scarce in some areas, those who do the procedure may travel great distances to far-flung clinics. Doctors concerned about their safety may not live near an abortion clinic.

Furthermore, abortion providers are often denied privileges at hundreds of hospitals with religious affiliations.