Forty years after the legalization of abortion in the United States, just four doctors offer controversial late-term procedures, and are the subject of a documentary at the Sundance film festival.

"After Tiller," named for physician George Tiller, a prominent practitioner of late-term abortions shot dead by an extremist in 2009, focuses on the few remaining doctors who perform abortions in the third trimester of a pregnancy.

The Supreme Court legalized abortion exactly 40 years ago -- on January 22, 1973 -- but granted states the right to limit abortions in the final three months of a pregnancy.

Although late-term procedures make up just one percent of all abortions in the United States, they are the most controversial, facing particularly virulent protests by abortion opponents.

Aside from death threats, such doctors face "institutional barriers," Dr. Susan Robinson, a former colleague of Tiller who still performs such procedures, told AFP following a screening of the documentary at Sundance, the annual independent film festival held in the western US state of Utah.

"If you do abortions, it is very hard to get the privilege to work in a hospital, because they don't like abortion providers. They are almost all done in outpatient clinics, free-standing clinics, in this country," she says.

"Being an abortion provider is very stigmatized. Other doctors look down on you and think of you as like the lowest of the low."

Robinson moved to New Mexico after Tiller's death to continue her work with another colleague. A third doctor practices in Maryland, after being expelled from Nebraska and Iowa, and a fourth has a practice in Colorado.

"We anticipated that one of the difficult aspects of this is of course being a target and having protests every day," said co-director Martha Shane.

"We didn't realize how emotionally draining the work is. Because you're dealing with these women who are going through one of the most difficult times of their life."

New Mexico law grants doctors full discretion over whether to carry out abortions -- most often requested in cases in which the fetus is severely malformed -- but Robinson says she relies on the judgment of the women themselves.

"If a woman comes to me, particularly if she struggles to get there, she's come from Canada or California, Louisiana or France, because she feels so strongly that she needs an abortion," she said.

"This woman has struggled with this decision, herself. She's not coming because she saw the clinic while she was on her way to the grocery store.

"Underlying all of what I do is the belief that women are capable of having ethical struggles, working on ethical questions and arriving at the best decisions for themselves."

Co-director Lana Wilson insists that Robinson "is a doctor. She's not there to be a moral arbiter."

"She's thinking about the safety and wellness of the patients that come to her. This is just not black and white and about judgment. It's about compassion."

Robinson and her colleague are training a 35-year-old physician to continue their work after they retire.

"We are thrilled. We would cheerfully train more doctors. It's not that the doctors don't know how to do this, but they are afraid."