After years of shifting more health-care expenses to workers to keep their own costs in line, companies are beginning to pull back on raising employee premiums and out-of-pocket charges.

Confronted by a tight jobs market, companies are reconsidering their reliance on high-deductible plans that force employees to pay large up-front costs before services are covered. They’re also becoming more active in seeking out ways to reduce costs for themselves and their employees.

Controlling health-care costs is a vital but illusive issue for companies, who provide coverage for about 153 million people. Medical costs continue to outpace inflation, putting stress...