A day after burglars made off with priceless jewels from a German museum, pressure is growing on police to find the culprits. One big reason: The diamond-encrusted dagger, pearl necklace, and dozens of other glittering artifacts—estimated to be worth more than $1 billion by the local press—were uninsured.

The German state of Saxony, the owner of the Green Vault museum in the eastern city of Dresden, carried no insurance on the jewels, standard practice because the premiums typically exceed potential damages in the long-term, the state Finance Ministry said Tuesday.

While public museums usually insure works of art that are loaned to other institutions, they often don’t take out policies on their permanent collections, according to Julia Ries, head of fine art and jewelry at insurer Ergo Group AG.

“The budgets of public museums are limited,” Ries said. “You can’t replace such a collection from a monetary or art-historic value. If the jewels aren’t recovered, this part of the collection will be lost forever.”

The insurance shortfall was revealed as more details of the theft became clear. Police believe the burglars set a fire nearby to create a power outage, then broke a window to enter the museum. Though the total number of culprits is unknown, two people quickly smashed a display case, snatched the loot, and fled.

The whole thing took “just a few minutes,” police said.

Bild, a daily tabloid, reported that the jewels are worth about 1 billion euros ($1.1 billion), without saying where it got the estimate. Museum officials have said the collection includes unique ensembles of diamonds that are of priceless art-historic value, declining to give a financial value.

Even as the scale of the loss became clear, some good news emerged: The thieves weren’t able to rip out all of the jewelry, some of which was sewn onto fabric lining the display cases. And one of the museum’s best-known treasures, the 41-carat Dresden Green Diamond, is on loan to New York’s Metropolitan Museum of Art.