FREMONT, Calif. -- Another long line of people snaked its way outside an H1N1 vaccine clinic in Fremont Saturday. But unlike previous events where hundreds of people were turned away, those patient enough walked away with what they came for.

For the second weekend in a row, Bay Area cities hosted H1N1 vaccination clinics and there are signs that some areas are starting to see supply meeting demand.

Officials say the response was overwhelming at the Fremont Senior Center Saturday morning, where thousands of people waited in line for roughly three hours, many with young children.

“For safety and we'll be traveling to India so we want him to be vaccinated,” said Prajakti Parasnis of Fremont, who brought her son to the clinic Saturday.

Pregnant women were brought to the front of the long line and new protocol was instigated -- a separate line was created for those not in the high-risk category.

Healthy adults started lining up as early as 4 a.m. to see if there was any extra vaccine, and by noon, the clinic announced it had enough vaccine for everyone standing in line, regardless of age and health.

Organizers say they made improvements to quicken the line and double the number of people vaccinated per hour from 200 to 400, bringing the total number of people vaccinated close to 4,000 Saturday.

“It's primarily targeted to alameda county residents that do not have insurance or any other way of getting the vaccine, but we're not turning anyone away at the door,” said Fremont Fire Captain Jeff Youngsman.

Alameda County hosted eight H1N1 vaccination clinics Saturday, drawing people from Fremont to Oakland. Organizers say they saw more patients and more help, including 60 volunteers at the Fremont clinic.

“I want to help out because that's what our family does is community service,” said Kathy Burgardt, an assistant principal from American High School. “We work for a disaster medical assistance team that goes on national crises and it's really important community service to get everyone vaccinated.”

Other Bay Area counties such as Santa Clara ran out of H1N1 shots last weekend and officials there are anticipating more crowds at clinics Sunday.