The fire that killed 112 workers at a garment factory in the suburbs of Bangladesh’s capital last month was a stark reminder of the human costs of producing and consuming cheap clothes.

While American officials have condemned poor safety conditions at the factory and have urged the Bangladeshi government to raise wages and improve working conditions, the United States can do much more: It should bring down high tariffs on imports from Bangladesh and other Asian countries, which put pressure on contractors there to scrimp on labor standards in order to stay competitive.

The United States imported more than $4 billion worth of apparel and textiles from Bangladesh last year. So it has an interest in giving the country’s garment industry some financial room with which to improve conditions for the three million employees, most of them female, who work in the industry.

Monitoring systems have, in many cases, achieved progress at the higher levels of the industry: the contractors that deal directly with American retailers. But oversight is lax, and conditions particularly dire, in factories run by subcontractors, like the Tazreen Fashions factory, the site of the deadly blaze on Nov. 24.

A bill introduced in Congress in 2009 by Representative Jim McDermott, Democrat of Washington, could have improved the situation by including Bangladesh, Cambodia, Laos, Nepal, Pakistan and Sri Lanka on the list of developing countries, like Mexico, that receive duty-free access to the American market as a result of free-trade agreements. But the bill never even made it to committee, and Bangladesh still faces a cost squeeze that is ultimately felt most acutely on those lowest on the production chain, especially the lowest-paying subcontractors, among whom corruption is endemic. It takes its greatest toll on workers.

The distortions created by the current trade policy are striking. In the United States federal fiscal year that ended in September 2011, Bangladesh exported $5.10 billion in goods to the United States, of which less than 10 percent were eligible for exemption from import duties. On the rest, Bangladesh had to pay at least 15.3 percent in tariffs. The tariffs were equivalent to imposing a $4.61 tax on every person in Bangladesh, a country with a per-capita annual income of $770.  This year, according to news accounts, Bangladesh will have paid more than $600 million annually in American tariffs, even as the United States Agency for International Development said it was committed to $200 million in development aid to Bangladesh.

Of course, no free trade legislation is controversy-free. One argument against reducing restrictions on Bangladeshi imports is that it might hurt even poorer countries, in sub-Saharan Africa, that enjoy duty-free access under a 2000 law, the African Growth and Opportunity Act. But studies have shown that extending duty-free access to South Asian goods would have negligible costs, yield huge benefits for Bangladesh’s economy and have minimal negative impact on African exports.

Bangladesh’s government and industries have a moral duty to prevent catastrophes like the November fire from ever occurring again. They need to insist that factory operators meet safety standards, that inspections are conducted honestly and that recommendations are enforced.

But leveling the playing field of international trade could advance all of these goals. International brands like Tommy Hilfiger, Gap, H&M, Target and Walmart demand low prices and fast turnaround. In that context, high tariffs work against the goals of fair-labor standards and factory safety.

In the fire’s aftermath, it’s tempting to focus only on local corruption and lax labor standards. But there have been positive changes in recent years; labor groups, businesses, nongovernmental organizations and even some international buyers have formed coalitions to improve safety at many factories. In a survey I conducted of garment workers at established factories, 62 percent said labor conditions had improved.

But for improvements in workers’ well-being to have lasting effect, tariffs on exports to the United States, the world’s largest consumer market, must be eased.