After ambitious new standards to improve the school lunches of millions of American students kicked in 2012, “lunch ladies” complained, kids turned up their noses and politicians railed.

The new standards, they said, would make kids abandon the school lunch program, force cash-strapped school districts to struggle to meet lofty new targets—and prompt kids to dump more food in the trash.

A new report issued Wednesday says the picture is hardly as bleak as those predictions. In fact, the report from the Pew Charitable Trusts and Robert Wood Johnson Foundation says that four out of 10 school lunch directors report having few or no problems implementing the standards, and six out of 10 say the same thing for school breakfasts.

“We know