Several states whose health exchange websites failed their first test during last year's inaugural ObamaCare open enrollment period have adopted different approaches for the second round, which began Saturday.

Some, like Oregon and Nevada, folded and decided to go with the federal exchange. Others, like Maryland and Massachusetts, fired their technology contractors and are hoping for better results this time.

It hasn't been cheap.

The original cost of Massachusetts' website was estimated at $174 million. That has jumped to $254 million. When launched, the website, designed by the same contractor that worked on the troubled Healthcare.gov, was incompatible with some browsers and was riddled with error messages and navigational problems. The problems were so bad, federal officials gave the state three extra months to meet the requirements of the Affordable Care Act. Gov. Deval Patrick issued a public apology and health care officials were forced to adopt a series of manual workarounds, creating a backlog of more than 50,000 paper applications.

Patrick told the Associated Press that there won't be a repeat of the disastrous roll-out this time around, saying the state has "been testing and retesting" the revamped website.

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Minnesota's state-run exchange, MNsure, wasn't ready for prime time when it launched in 2013. Some of the technical glitches that frustrated consumers remained unresolved by the time the open enrollment period closed. MNsure officials are promising a better experience this time -- with more call center workers and a website that's 75 percent faster. But they also acknowledge the system won't be perfect.

California's exchange also was ill-prepared to handle the high volume of calls, triggering long wait times at help centers and forcing the state to extend open enrollment for two weeks beyond the original March 31 deadline.

"It swamped us," said Covered California Executive Director Peter Lee, promising increased website capacity and extra call center staff.

Maryland's website crashed on the day it opened last year. The state decided there were too many bugs to completely fix Maryland's original system for the new enrollment period, and the board overseeing the exchange fired its prime information technology contractor and is transitioning to a new system with technology used by Connecticut.

The problems at Washington state's health care exchange occurred after people signed up for insurance. At least 24,000 people who obtained private insurance couldn't use that coverage when they went to the doctor because of problems crediting payments and sending those dollars on to insurance companies.  It took about nine months to fix those problems.

In Vermont, officials announced in August they were scaling back their relationship with the prime contractor on the state's exchange, CGI, reducing the company's role from developing and hosting the Vermont Health Connect site to just hosting it.

Development of the site was switched to another contractor, Optum, the same health care technology firm retained by Massachusetts to revamp its website after it also cut ties with CGI.

Other states fared better.

Colorado's exchange experienced minimal disruptions and the state was able to sign up about 148,000 people.

Kentucky also had a successful rollout, signing up more than 421,000 people for health insurance during the first round of open enrollment. Obama even pointed to Kentucky as an example of the success of his health care law during his State of the Union address this year.

The states were so successful that when Massachusetts was casting around for solutions to its website troubles, it looked to Kentucky and Colorado for what it called "a proven, off-the-shelf solution."

Connecticut was also able to claim bragging rights: After the launch of its marketplace, Access Health CT, officials there predicted the state's uninsured rate would drop to from 7.9 percent to 6.5 percent. Instead it fell to 4 percent.

"We had an office pool going on about what this percentage was going to look like," said Access Health CT CEO Kevin Counihan. "No one expected we'd be down to 4 percent."

In Massachusetts, the experience of finding insurance through the website is beginning to turn around for some.

Christopher Doty lost his insurance when he lost his job in marketing last month. The 32-year-old Boston resident, who has asthma and needs medicine on a regular basis, said he was quickly able to sign up for insurance through MassHealth, the state's Medicaid program.

"Losing my job and knowing I needed some kind of health insurance at first was super-stressful," Doty said. "I basically had coverage within a couple of days."

On Sunday, Health and Human Services Secretary Sylvia M. Burwell told NBC's "Meet the Press" that 100,000 people had submitted new applications this weekend via the federal website serving 37 states. That's a big difference from last year, when only a handful of customers managed to enroll on the first day.

Burwell also said that a half-million people who already have coverage through the program were able to log into their accounts this time.

There were reports Saturday that returning customers had problems, but some of that may have been confusion trying to remember user names and passwords.

Patrick said one way to avoid future problems is heightened vigilance.

"Outsourcing and privatizing -- this is not the solution." Patrick said. "The solution is to make sure that there's very close oversight even when we use an outside vendor."

The Associated Press contributed to this report.