President Trump’s shake-up of the Department of Homeland Security’s leadership shows he wants to double down on control of the border. That’s a good idea but only if he is more sensitive and creative in how he goes about it.

Immigration is important to Trump because it is important to his voters. Polls regularly show it is the first or second priority among Republicans. While they surely give him credit for fighting, many also expect him to win, or at least succeed in stemming the flow of migrants crossing the border illegally to a much greater degree than he has done so far. Hence, the forced resignation of Homeland Security Secretary Kirstjen Nielsen and other pending DHS departures.

Trump has nevertheless failed to put serious political pressure on Democrats to meet him halfway in addressing the border crisis. They see polls showing their own base adamantly opposed to almost every immigration measure Trump supports, and they see no political reason to compromise. (Thus, the five-week standoff during the government shutdown earlier this year.)

Politics 101 should lead Trump to seek ways to make the swing voter come over to his side. So far, though, he has not even tried to do that. Stories of crimes committed by undocumented immigrants and pictures of “angel moms” at news conferences may move his base but not the middle. And some things Trump does anger the middle and upset some of his base, such as the policy of separating children from their parents at the border.

Some reports stated that Trump was considering re-adopting this politically suicidal policy under the belief that it is effective at deterring migration by families. It’s good that the president now denies any such plans, as they would be extremely politically tone deaf. The border separation policy was one of the few administration policies that led to widespread, bipartisan condemnation. Even some of evangelical Christian leaders who otherwise support Trump disliked it. Restarting the policy — or even hinting at anything close to cruelty toward children — would immediately reopen the hornet’s nest.

Trump should instead work within the confines of public sentiment to find new friends. America’s middle wants to control the borders and enforce the law humanely. There are a couple of ways to do that sitting right under the president’s nose.

The first is to start a voluntary program of employers who use E-Verify, which ensures that employees are legally able to work in the United States. A voluntary program should be modeled on the Energy Star program, which allows manufacturers of appliances that meet energy saving standards to advertise that fact with an “Energy Star” appellation. How about a program that would similarly permit employers to advertise that 100 percent of their employees are working legally? Such an appellation would let people know which contractors comply with the law, putting social pressure on others to do so, as well.

The second policy is to restrict the ability of undocumented immigrants to send money back to their home countries. The vast majority of undocumented immigrants come to work, and some of the money they earn here illegally is sent back to support their families. According to the Pew Research Center, more than $46 billion was sent home to Mexico, Guatemala, Honduras and El Salvador from the United States in 2017. These figures were a bit more than 1 percent of Mexico’s gross domestic product in 2016, but between 10 and 20 percent of the other three countries’ GDP. To the extent these remittances come from undocumented workers, restricting them will give the administration significantly more leverage with those nations’ governments than anything currently contemplated.

The administration should immediately scour the law to find what authority it has to impose reasonable restrictions on this practice. People who send international remittances are normally already required to show a government-issued ID, such as a driver’s license; proof of residence, such as a utility bill; and a Social Security number. Perhaps the Internal Revenue Service or the Consumer Financial Protection Bureau has the authority to also require proof of legal residence, production of a passport or mandatory use of E-Verify to ensure the Social Security number provided is valid.

Both of these measures would likely be as or more effective at drying up demand for undocumented workers, who comprise the overwhelming majority of people illegally crossing the border, than any amount of border-control policy or raids by border Immigration and Customs Enforcement agents. They are also more humane, and might work in Trump’s favor politically. The extent to which economic hardship might impact undocumented immigrants could cause a backlash among Democrats, offering the president leverage to negotiate seriously with them without unduly harming his image among swing voters.

They say the definition of insanity is doing the same thing over and over and expecting a different outcome. Trump likes to surprise his adversaries and use that unease to place them at a disadvantage. Shaking up his approach to fighting illegal immigration could give him the long-sought win that has so far eluded his grasp.

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