SANTA FE, N.M. — For years, New Mexico has had one of the highest rates of alcohol-related traffic deaths in the nation. And during each legislative session, it seems, lawmakers wrestle with how to make the state’s highways and rural roads safer, usually spurred by the latest horrific accident.

This week, an aggressive new bill was being considered that would forbid many people convicted of drunken driving from buying alcohol anywhere — stores, restaurants or bars. If it passes, it would be among the most restrictive drunken-driving laws in the nation.

Under a 2005 New Mexico law, people convicted of drunken driving are required to install ignition interlock devices in their vehicles, typically for one year for a first offense. Drivers have to breathe into the device to start the ignition, and it does not allow the car to start if it detects a threshold level of alcohol on the driver’s breath.

The current proposal would expand that measure, barring thousands of New Mexicans who are required to have the devices from buying alcohol at all. Under the measure, drivers with the interlocks would be issued a specially marked license indicating that they are prohibited from buying alcohol.