Three years after Michelle Obama launched her Let’s Move! campaign, the fight against childhood obesity faces a tactical problem. Recent years have seen dipping obesity rates in a few places, including New York, Mississippi and Philadelphia. But 17% of American children are still obese. The question is how to speed up progress. Further bans look increasingly unlikely.

Voluntary programmes remain politically much easier. Mrs Obama has exhorted firms to take action. Many companies have. On March 6th the Partnership for a Healthier America, a business group, published a report praising its members for putting more grocers in poor areas and healthier foods at restaurants. Sixteen food and beverage companies have promised to slash a combined 1.5 trillion calories from their products by 2015. Their first progress report is due in June. The long-term effect of these efforts may be slim. For example, even if the food and drink firms keep their promise, they would cut just 14 calories from the average American’s daily diet.

Regulations might bring bigger change, but recent years suggest that such rules will come slowly, if at all. Congress did pass a law requiring healthier school lunches, though its effects are limited. Other attempts at national regulation have stalled. Four federal agencies studied voluntary guidelines to limit junk-food advertisements to children. Under pressure from Congress, the agencies dropped the effort. Obamacare requires that all restaurants and cinemas post the number of calories in their foods. The Food and Drug Administration proposed a rule for menus in 2011, but has yet to finalise the regulation.

Cities and states are more likely to act than Congress (hardly a high bar), but they face their own challenges. Last year the beverage lobby spent more than $2.8m to defeat a soda tax in the small city of Richmond, California. Even Mr Bloomberg, the anti-obesity crusade’s most fervent warrior, can only do so much.

He and his health commissioner, Thomas Farley, have already improved school lunches, installed bike lanes and paid for revolting posters that show soda turning to fat. Their efforts seem to be working. From 2003 to 2011 obesity rates among poor four-year-olds dropped from 20% to 17% (see chart). Obesity rates in older children dropped 5.5% from 2006 to 2011, though mostly among richer ones.

Mr Bloomberg wants to do more. But New York state rebuffed his bid for a statewide soda tax. Federal regulators rejected his attempt to ban the purchase of soda with food stamps. Now his size limit may be scrapped in court. Other cities are watching closely. If it can fail in New York, it will fail anywhere.