In a lush valley surrounded by the Peruvian Andes — past two sets of security gates, high fences, barbed wire and a rigorous pat-down — 13 women stood hard at work. They were weaving and knitting luxurious alpaca wool sweaters, deep-pile roll-necks and silky-soft track pants, destined to be sold to wealthy shoppers with lives far away, and a far cry, from their own.

All were prisoners at the women’s penitentiary center in the city of Cusco, serving long sentences predominantly for drug-related crimes as well as murder, human trafficking and robbery. They were also employees of Carcel, a Danish brand founded in 2016 specifically to provide incarcerated women with jobs, training and, possibly, a crime-free future.

More than two years into their program, both Carcel’s founders and the Peruvian prison authorities say the project has been a measurable success. It’s popular with prisoners and consumers alike and proof that the profitable and responsible production of luxury fashion can have a place behind bars.

Peru is becoming something of a case study on the issue of aid versus exploitation. A little more than 5,000 women are currently incarcerated there, and over 50 percent are actively employed in producing leather goods, clothing and textiles, according to INPE, the national penitentiary institute.

Yet questions around the ethics of prison labor and regulation have also made headlines of late. There have been reports of Muslims incarcerated in brutal Chinese internment camps producing sportswear apparel, and strikes against imposed labor for paltry wages in American prisons. This month, tensions flared on social media when Carcel introduced a new line of silk garments produced from women’s jails in Thailand.

“Companies are literally advertising that they use slave labor now as a reason you should buy their product,” one person wrote on Twitter, prompting a chorus of outrage from hundreds.

“Your ‘sustainable business model’ includes the need for women to be in prisons,” another user wrote, followed by a slew of confused-face emojis. The more Carcel posted explanations on its practices, payment models and prices, the angrier the online responses became.

The long history of fashion and prison

“Prison labor is a very complicated and opaque topic,” said Peter McAllister, the executive director of the Ethical Trading Initiative, an alliance of companies, trade unions and nongovernmental organizations that back workers’ rights.

“On one hand, there are definitely well-intentioned brands with rehabilitation programs in place doing some good work all over the world,” he said. “On the other hand, there are big questions to be asked around whether inmates should ever form the mainstream production of a profit-driven label, particularly given how many unacceptable cases of prisoner exploitation exist deep in the global fashion supply chain.”

Fashion has a long-established history in prisons, dating back to the 1700s. Traditionally, most manufacturing programs in countries like the United States or Britain were run either by government bodies or correctional boards in order to mass-produce low-value items at scale, like military uniforms. Inmates received well below the minimum wage, if anything at all. In the 1990s, with a record number of people behind bars in many countries, there was a boom in private companies employing prisoners for tasks as varied as telemarketing, the manufacturing of circuit boards, and garment production for brands like Victoria’s Secret and J.C. Penney.

Today, in Britain, the average prisoner engaged in some kind of employment earns around £10 a week, a government report from 2016 found. In the United States, the value of prison labor to the economy continues to add up — though not for inmates. The Bureau of Prisons operates a program known as Federal Prison Industries that pays inmates roughly 90 cents an hour to produce mattresses, eyeglasses, road signs, body armor and other products for government agencies, earning $500 million in sales in 2016.

The made-behind-bars trend

One product subcategory in particular has been gaining international traction in recent years: small, street trend-oriented brands selling clothing made by inmates, like Prison Blues in the United States, Stripes Clothing in the Netherlands and Pietà, another Peru-based label. All claim they can create a profitable and sustainable business model while also providing new jobs and opportunities for prisoners.

Pietà was founded in Lima in 2012 by Thomas Jacob, a Frenchman who had once worked for Chanel, and currently employs around 50 male and female inmates from some of the largest jails in Peru. Prisoners manufacture anti-establishment logo T-shirts, sweatshirts, hand-knit sweaters, varsity jackets and high-top sneakers using locally sourced materials. Prices range from $8 for tote bags to $120 for jewelry.

“There are a lot of men and women in jail very far from the image you may have of inmates, who just want to get by, to learn a skill, to work, to earn money,” said Mr. Jacob, who has opened five Pietà stores in the Peruvian capital and says he is considering an international expansion.

Inmates don’t just make the clothes, he said — on occasion they also contribute to his designs, giving them both a creative outlet and training. Often, they act as models for advertising campaigns and are paid a portion of the sale price for each unit of clothing they produce, providing income they can send home to their families. Upon release, former inmates can continue working with Pietà, or seek jobs at other companies with Pietà’s recommendation and support.

Louise van Hauen and Veronica D’Souza, the founders of Carcel (which means “prison” in Spanish), met while living and working in Kenya. The former was a creative manager at a leather bag company and the latter was the head of a social start-up that made and distributed menstrual cups.

Ms. D’Souza said a visit to a women’s prison in Kenya in 2014 changed her thinking. “It became clear to me that virtually all of the inmates were mothers who were there because of poverty-related crimes, be it theft or prostitution. The same applies here in Peru,” she said. As part of the drug-production chain in Latin America, cocaine paste must be transported from crop areas in remote parts of the country by drug mules. Many are women, and often, they are nonviolent, first-time offenders. According to INPE, 85 percent have children to support at home.

“Often these women get incarcerated, then released, but struggle to find ways to provide for their children, and the crime cycle would start all over again,” Ms. D’Souza said. “The system was clearly broken. It got me thinking about how we could create a new model that might break the cycle.”

Ms. van Hauen said she wanted to start somewhere with proximity to high-quality natural materials, where some of the skills required were already part of local culture.

“As one of the world’s largest alpaca wool exporters, and a country where knitting is a national pastime, Peru was perfect,” she said. Instead of designing streetwear, though, she and Ms. D’Souza decided to focus on the luxury end of the market.

“Historically, lots of brands have struggled to make a profit or scale because of the low quality of product or design,” Ms. van Hauen said. By having inmates create goods of higher value, the thinking goes, the products have better retail viability and healthier profit margins — and the women hone a more worthwhile skill set.

Virginia Matamoros, the director of Cusco Female Penitentiary, said that the prison offered basic training in sewing, weaving, baking and gardening to all new inmates with the hope that they can then move on to working with companies that can prepare them for release.

“We accepted Carcel because it is an organized, formal company that works with good salaries and which has subsequently pushed the other companies that operate here to improve their pay rates and work schedule,” she said. Ms. Matamoros added that increased access to work opportunities could lessen the likelihood of recidivism. “More than anything, it is extremely positive for their self-esteem,” she said.

‘I do this to overcome my past’

In Cusco, the Carcel inmates are trained by more experienced weavers until they have developed the vocational skills to work a five-hour shift, five days a week. They earn cash salaries of 650 to 1,100 Peruvian soles ($180 to $329) per month, depending on their level of experience. Earnings in both Peru and Thailand are benchmarked against the national minimum wage. In Peru, this is 930 soles a month.

“The women who work for us earn the same as an elementary schoolteacher here,” Ms. D’Souza said. “We believe that a fair job inside of prison should be equal to a fair job outside of prison.”

The prison takes a 10 percent cut of inmates’ wages. The workers keep a portion for living expenses like food and soap, and Carcel pays the rest into their families’ bank accounts. Beyond the base salary, women can also receive bonuses for the quality of their work, good behavior and overtime.

“When I got here eight years ago, this prison was a really sad place,” said Teodomira Quispe Pérez, 51, a widow and mother of six who has five more years to serve of a sentence for drug trafficking. She now oversees quality control in the Carcel workshop. “I am looking forward to getting out and buying my own machine. Working in this textile workshop takes me away from my imprisonment,” she said, folding an order of $190 baby alpaca T-shirts bound for Net-a-Porter. The luxury e-commerce platform started to stock Carcel last summer.

“I do this to overcome my past and push forward for my daughter’s sake because I am hoping I can be with her again someday,” said another inmate, Flor Rosa Quispe Jacinto. Ms. Jacinto, 28, is in charge of training new workers in the three workshops and one classroom run by Carcel. Ms. Jacinto, who said she felt too ashamed to disclose the nature of the crime that put her in prison, showed off labels inside the garments that are printed with the name of both Carcel and the women who made it.

It can sound too good to be true. “Prisoners by nature of their position are cut off from the rest of the world,” said Mr. McAllister. “They don’t have a voice. So the only stories you will ever hear from inmates about prison labor tend to be good ones, vetted by the companies or authorities involved.” (None of the 11 inmates interviewed by The New York Times appeared to have been coerced or coached.)

There is no question the work is selling. According to Elizabeth von der Goltz, the global buying director of Net-a-Porter, fashion brands with social purpose are increasingly popular with shoppers.

“Nearly all our Carcel styles sold out globally in just the first two weeks of launch, while the baby alpaca T-shirts are continuing to sell out week after week,” she said.

To meet demand, Carcel is now looking to double its staff base in the Peruvian prison. At the company’s second production base in Thailand — the country with the most female inmates in the world — e-banking accounts are being developed for some prisoners and their relatives to minimize siphoning from wardens or companies. Carcel said it hoped to operate in a further three to five countries within the next five years.

Considerable challenges remain. This week, Carcel halted sales in America when it became aware of a federal law that bans the import of goods made by convicts. The company is now seeking a waiver; it pointed out that the United States is one of the few countries that did not ratify a 2014 International Labor Organization convention on forced labor, despite domestic prison labor being legal. Net-a-Porter confirmed Wednesday that it would suspend Carcel sales until the issue was resolved.

“The I.L.O. states on its website: ‘a good indication of whether prisoners freely consent to work is whether the conditions of employment approximate those of a free labor relationship,’ and that is what we root the principles of Carcel upon,” Ms. D’Souza said from Copenhagen during a phone interview. “We treat them as employees of a company, not prisoners in a jail.”

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