Tens of thousands of immigrants who are in the U.S. illegally but don’t have serious criminal records could be shielded from deportation under a policy change being weighed by Homeland Security Secretary Jeh Johnson.

The change, if adopted following a review ordered by President Barack Obama, could limit removals of people who have little or no criminal record but have committed repeat immigration violations such as re-entering the country illegally after having been deported, or failing to comply with a deportation order.

The possible move, confirmed by two people with knowledge of the review, would fall short of the sweeping changes sought by activists. They want Obama to expand a two-year-old program that grants work permits to certain immigrants brought here illegally as children to include other groups, such as the parents of any children born in the U.S.

John Sandweg, who until February served as acting director of U.S. Immigration and Customs Enforcement, said he had promoted the policy change for immigrants without serious criminal records before his departure and said it was being weighed by Johnson. An immigration advocate who has discussed the review with the administration also confirmed the change was under consideration. The advocate spoke on condition of anonymity because the proceedings are confidential.

“Any report of specific considerations at this time would be premature,” Clark Stevens, a spokesman for the Homeland Security Department, said Monday. Stevens said Johnson “has undergone a very rigorous and inclusive process to best inform the review,” including seeking input from people within DHS as well as lawmakers of both parties and other stakeholders.