Checks for $5,100 to $10,000 written to Americans who bought Volkswagen diesel cars equipped to fool emissions tests may appease those owners, but they hardly constitute a victory for clean air. Rather than declare the matter closed, regulators in the United States and Europe need to redouble efforts to end all varieties of test-gaming in the auto industry.

Since VW’s “dieselgate” broke last September, Mitsubishi has admitted it cheated on fuel-efficiency tests, and Renault recalled 15,000 vehicles with faulty pollution-filtering systems. And independent studies of real-world driving, as opposed to laboratory testing, have found that brands including Honda, Hyundai, Mazda, Nissan and Volvo emit more greenhouse gases than advertised.

In Europe, oversight of testing is left to individual nations, leading to longstanding complaints that governments favor their own domestic brands. Testing both there and in the U.S. is done mostly by private firms hired by the car companies.

In the U.S., where there are relatively few diesel vehicles, diesel pollutants like nitrogen oxides are not as big a concern as carbon dioxide emissions. On average, vehicles in the U.S. give off 24 pounds of climate-warming gases for every gallon of fuel burned. So U.S. authorities need to broaden their scrutiny of fuel-efficiency testing.

And as anyone with a daily commute can attest, the miles-per-gallon numbers written on showroom stickers are pure fantasy. Just this week, U.S. carmakers urged federal and California regulators to ease future mileage standards, admitting their failure to live up to an agreement reached in 2011.

The car companies will do anything they can to beat tests, and lax rules play into their hands. Regulators need to clamp down or risk losing major battles against air pollution and global warming.