Dr. Alan Sheff, who charges patients an additional $1,800 a year, is able to spend more time with his patients.

NEW YORK (CNNMoney)

Patients can receive this type of comprehensive service from a growing number of primary care doctors who've switched to concierge medicine. But it comes at a price, often hundreds or thousands of dollars a year, and at a time when many Americans are already struggling to afford their insurance and medical care.

Concierge doctors generally charge patients a membership fee -- typically $1,800 a year -- outside of the traditional insurance system. They often have fewer patients -- usually no more than 600, compared to 2,500-plus for a typical physician -- so they can spend more time with each one.

Beyond those common traits, there are many models of concierge medicine, which is also called private physician or direct pay practices. Some doctors target the wealthy, charging five-figures to handle all aspects of their health care, from negotiating bills with hospitals to being in the operating room. Others charge a flat rate of $50 a month for appointments.

For some physicians, the annual fee covers all office visits. At other practices, it only buys patients a comprehensive yearly exam, as well as same-day appointments and after-hours access.

Whatever the model, patients still need traditional insurance to cover specialists' visits, hospitalizations and other diagnostic testing, such as MRIs.

Related: Paying thousands before health insurance even kicks in

Many doctors shy away from the term "concierge" because it connotes that it's for an exclusive club. They are not practicing "wealth care," as a few of those interviewed termed it.

Instead, these doctors are increasingly positioning themselves as health care providers for middle class Americans who value wellness.

Read more here:

'Wealth care' or next big thing in medicine?