The insurance industry says it wholeheartedly embraces a health care overhaul, promising Congress and the president that it will make it much easier for individuals to buy insurance on their own.

Insurers, for example, have agreed to sell policies even to people with pre-existing medical conditions, and to stop basing prices on how healthy or sick someone is. These sweeping concessions would help legislators achieve their goal of putting health coverage within reach of many of the nearly 50 million individuals who currently have none.

But so far, the industry has made no such promises about another segment of the health insurance market, one responsible for many people being uninsured in the first place: the market for small employers. By some estimates, about half of the nation’s uninsured are people who are self-employed or work for a small business.

In other words, policy analysts and others say, unless the insurance industry is willing to give some of the same ground to small businesses that they have ceded to individual policy holders, a big part of what is wrong with the nation’s health care system may not get fixed.