Four American women have received womb transplants from living donors at Baylor University Medical Center at Dallas, TIME learned exclusively. This is the first time living-donor womb transplants have been performed in the United States.

The four surgeries took place between Sept. 14 and Sept. 22, and three of the womb transplants were removed after tests determined the organs were not receiving normal blood flow. One woman still has her transplanted uterus and has shown no signs of rejection so far.

Uterus transplants with live donors have a precedent for success. In Sweden, where the surgery was pioneered, five of nine womb transplant recipients have given birth to healthy babies and one woman is pregnant for the second time.

Dr. Giuliano Testa, the lead surgeon and surgical chief of abdominal transplantation at Baylor, acknowledges that these results so far, while disappointing, still show tremendous progress. “If you look at this from the science [perspective], it’s something we’ve learned a lot from, and we have a patient who is doing well,” he says. “This is the beginning of hopefully a great history for medicine. ”

All four of the women have a condition called Mayer-Rokitansky-Küster-Hauser (MRKH) syndrome and were born without a uterus. About one in 4,500 women in the U.S. are estimated to have MRKH. Baylor plans to perform a total of 10 womb transplants before the end of 2016. “You cannot discount the desire of a woman to have a normal pregnancy, bear her own child, and deliver,” says Testa. “This is part of human nature.”

Baylor says the women received their transplants from so-called altruistic donors, meaning the donor women are not related to the recipients and do not know who they are. The women who received the transplants are between ages 20 to 35, and the donors are between ages of 35 to 60. Around 50 women volunteered to donate their womb. “I am totally amazed by that,” says Testa. “They told us, ‘We had our chance to become mothers, and now we have this uterus and it’s not doing anything for us. We can put this uterus to use for people who really need it.’ That struck me as a physician. These women are phenomenal.” Baylor has not identified any of the women.

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The donors and the recipients declined to speak with TIME, requesting privacy.

This is the second time a hospital in the U.S. has attempted womb transplants. In February, the Cleveland Clinic performed the first uterus transplant in the U.S.; the organ was from a deceased donor. Less than two weeks after the transplant, the recipient, Lindsey McFarland, acquired an infection and the transplant had to be removed. The Cleveland Clinic then put its program on pause. You can read TIME’s interview with McFarland, here (for subscribers). Uterus transplants are estimated to cost from $150,000 to over $500,000, and since they are still experimental, they are not usually covered by insurance.

At Baylor, it took about five hours for the wombs to be removed from the donors, and another five to transplant. The surgical team included four Baylor University Medical Center surgeons, two Swedish surgeons with womb transplant experience, two anesthesiologists, and seven operating room nurses.

The two Swedish doctors are from Sahlgrenska University Hospital in Gothenburg and are part of the first surgical team in the world to perform successful womb transplants. “We have to collaborate with other teams around the world and share our knowledge,” says Dr. Liza Johannesson, one of the doctors from Sahlgrenska University Hospital who assisted Baylor with their surgeries. “If no one can repeat it, it’s not worth anything. We owe it to the patients to be open.” Johannesson says her team will continue to assist Baylor with further womb transplant procedures.

Baylor estimates it will take the women about three months to get back to normal daily activity. In six to 12 months, a woman with a successful uterus transplant can attempt in vitro fertilization (IVF). (Since the women’s ovaries are not connected to their wombs, IVF is required if she wants to get pregnant.) Because all organ transplants require recipients to take potent and sometimes toxic anti-rejection medication, typically, the uterus is removed after they’ve had two children.

The Baylor team is assessing the results from the first four surgeries before moving forward with the other six. “This is the way we advance,” says Testa. “I am not ashamed of being the one who will be remembered as the guy who did four [transplants] in the beginning and three failed. I am going to make this work. I believe from an ethical and clinical and research point of view, we have our heart in the right place.”

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