“The floor for Republicans has been raised,” Representative Tom Emmer of Minnesota, the chairman of House Republicans’ campaign committee, said in an interview. “Our incumbents actually are getting stronger districts.”

Congressional maps serve, perhaps more than ever before, as a predictor of which party will control the House of Representatives, where Democrats now hold 221 seats to Republicans’ 213. In the 12 states that have completed the mapping process, Republicans have gained an advantage for seats in Iowa, North Carolina, Texas and Montana, and Democrats have lost the advantage in districts in North Carolina and Iowa.

All told, Republicans have added a net of five seats that the party can expect to hold while Democrats are down one. Republicans need to flip just five Democratic-held seats next year to seize a House majority.

“They’re really taking a whack at competition,” said Michael Li, a redistricting expert at the Brennan Center for Justice.