Shipments of goods across the English Channel are recovering, with fewer haulage companies pulling out of jobs in the past week.

The rejection rate for cargo shipped from France to the U.K. fell to the lowest since the last week of November, an indication of reduced friction at the border, according to the the logistics company Transporeon.

The figures suggest that companies are adapting to new customs rules put in place on Jan. 1 following Britain’s exit from the European Union. Since then, truckers have been required to fill out forms and undergo checks at the border for the first time in decades. The high-frequency data supports the government’s assertion that freight flows are returning to normal.

(Read Matt Miller’s January article: New Brexit-era regulations add “red tape” and confusion to EU-UK trade)

“Market players have slowly commenced adjusting to the new circumstances,” said Transporeon Chief Executive Officer Stephan Sieber.

Truckers complain that the rules have made trips to the U.K. much less profitable. About 40% of lorries are returning to the continental Europe empty because of the cost and complexity of filling out paperwork, according to Rod McKenzie, managing director of policy and public affairs for the Road Haulage Association.

That observation, based on anecdotal evidence, is “not normal or a triumph,” he said.

The Transporeon data show a more upbeat picture. Demand to transport cargo from France to the U.K. increased last week to 17% more than the average in the third quarter.

Internal government figures first reported by the British Broadcasting Corp. showed that traffic coming into the U.K. was at 99% of last year’s levels.