Almost a decade ago, California became the first state in the United States to ban single-use plastic bags in an effort to tackle an intractable plastic waste problem.

Then came the reusable, heavy-duty plastic bags, offered to shoppers for ten cents. Designed to withstand dozens of uses, and technically recyclable, many retailers treated them as exempt from the ban.

But because they didn’t look much different from the flimsy bags they replaced, lots of people didn’t actually reuse them. And though they came emblazoned with a recycling symbol, it turned out that few, if any, actually were recycled.

The unhappy result: Last year, Californians threw away more plastic bags, by weight, than when the law first passed, according to figures from CalRecycle, California’s recycling agency.

Now, lawmakers are trying to fix that. A new bill seeks to ban all plastic bags offered at the checkout line, including the heavy duty kind. (Shoppers would still be able to pay for a paper bag.)

“It’s time for us to get rid of plastic bags all together,” said State Senator Ben Allen, a Democrat and a sponsor of the bill.