There haven’t been any regulations or new policies issued in response to the president’s “Buy American and Hire American” executive order, but there are signs it’s being implemented through back-door channels.

The order requires the federal agencies in charge of immigration to ensure that H-1B visas are awarded to the “most-skilled or highest-paid petition beneficiaries.” The temporary visas, which are reserved for “specialty occupations,” currently are awarded according to a random lottery.

But some immigration attorneys are noticing a shift...