Greenberg is well versed in consumer information. Nearly a century ago, the league initiated its White Label campaign. While it lasted, Greenberg said, it identified stores that provided fair wages and working conditions, and apparently was "hugely popular and very chic."
The disasters in Bangladesh have heightened contemporary consumer interest in the issue of ethical sourcing for clothes. Earlier this month, for example, shareholders had to walk through demonstrators at Gap's annual meeting demanding that the company sign a new Bangladesh factory safety accord. (Wal-Mart and many other major U.S. retailers also have so far declined to sign the pact.)
(Read More: European, US Retailers Split on Bangladesh Reform Plan)
Even before the Bangladesh tragedies, consumers' demand for ethical clothing was brewing. In a 2012 study, researchers from M.I.T. and Harvard looked at the effect of different signs describing clothes in 111 Banana Republic factory stores, some emphasizing the fair labor standards for manufacturing the clothes, and others emphasizing their fashion appeal.
For the lower-priced items the researchers tested, the signs made no difference in relative sales. But for the higher-priced item they measured—a $130 women's suit—sales increased 14 percent in stores with the fair labor signs.
"Even in this outlet setting there is a segment of shoppers who respond positively to a message conveying information about fair labor standards in factories making apparel," the researchers concluded.
That interest is also clearly apparent on college campuses where Alta Gracia, a clothing line from Knights Apparel, is sold. Knights, the largest supplier of college apparel, started Alta Gracia, which is produced by workers in the Dominican Republic who are paid a living wage, less than three years ago. And CEO Joe Bovich says it is now in 800 college bookstores.
Bovich aims to expand Alta Gracia's reach into mainstream stores. "It could be with the Alta Gracia brand, or it could be manufactured as private label," he said. "I think if we can get it out there, we're going to see the same response we've seen in the college bookstore market."
For now, the best way to find ethically sourced clothing is online, where small companies sell clothing directly sourced from ethical producers. You can also check the list of retailers involved with the Better Cotton Initiative, whose stated goal is to "make global cotton production better for the people who produce it, better for the environment it grows in and better for the sector's future." The list of companies that have signed the Accord on Fire and Building Safety in Bangladesh offers other possible options.
(Read More: H&M, Others Back Bangladesh Safety Accord)
_ By CNBC's Kelley Holland