That is a boon for people like Jennifer C. Graham, a single mother who was laid off in December with just five weeks of severance pay. Ms. Graham, who was a senior associate at a Manhattan interior design firm, immediately signed up for Cobra to make sure that she and her twin girls were covered. But the $966 monthly payments ate up more than half of her $1,600-a-month unemployment benefit.

“It’s completely ridiculous,” she said. “How can people get back on their feet?”

With the stimulus relief, her payments will soon fall to a more affordable level: $338 a month. Ms. Graham, who has an M.B.A., says she hopes to have a new job before the nine-month subsidy ends.

Another change under the stimulus package is that if you qualify for the subsidized Cobra benefit, you can also switch into a lower-cost health plan, like an health maintenance organization, if your former employer offers one, even if you were signed up for a more expensive plan while you were working.

For fuller details on the new Cobra provisions, see this Congressional Web page: http://edlabor.house.gov/blog/2009/02/health-coverage-for-the-unempl.shtml

If you, or someone in your family, has a pre-existing condition ...You can use Cobra to your advantage, even if you don’t qualify for the new subsidy.

Let’s say you have diabetes, but the rest of your family is healthy. Insurers will charge your family more than the average rate, because you are considered a high risk. In this case, you could stay on Cobra at an individual rate, and buy private insurance for the rest of the family. Look for policies at a large insurance broker site like eHealthInsurance.com, which offers more than 10,000 plans. Put in your sex, ZIP code and date of birth and the site will tell you which plans are available in your area. Many of them have been reviewed by customers, and you can apply online.

If you have children ... Explore keeping yourself and your spouse on Cobra, or buying private insurance, and enrolling your children in the federally financed CHIP program, suggests Ron Pollack, executive director of Families USA, a nonprofit consumer advocacy organization.