The country's second largest health insurance provider, Laya Healthcare, is to cut the cost of some of its policies by up to 19%.
The reductions will apply to 12 of the company's products from 1 January.
The insurer is also announcing details of three new schemes, which it is introducing in response to Minister for Health Leo Varadkar's call for insurance companies to help restore affordability to the market.
Prices on the three new schemes will be frozen for up to two years.
Health insurance analyst Dermot Goode says a return to some kind of price stability is now to be seen in the market, but he has urged consumers to be careful when choosing a plan.
More than 400,000 health insurance policies are due for renewal in January.
"I think the days of 20 to 25, and even 40%, increases are gone. People can now expect increases of maybe 5 to 7.5% - which for most consumers is acceptable. This is good news.
"The only thing I would say is I've seen some of the plans they're reducing the rates on, and of those 12 plans, eight of them are not good-value plans, even with the reductions.
"So people need to be very careful. Just because they see a price reduction, it doesn't mean that's the best plan."