MORE than 20m travellers reach America each year without having to apply for a visa, most of them from Europe. Perhaps 5,000 European citizens are estimated to have travelled to Syria and Iraq to fight with such terrorist groups as Islamic State (IS)—among them several of the attackers behind last month’s blood-soaked attacks in Paris. So it was little surprise that the House of Representatives voted overwhelmingly on December 8th to tighten the rules governing America’s visa waiver programme, under which citizens of 38 countries may enter the country for up to 90 days by applying for an Electronic System for Travel Authorisation (ESTA).

The House measure, which had White House backing and is similar to a bipartisan bill proposed in the Senate, would—once it becomes law—oblige anyone who has travelled since March 2011 to Syria, Iraq or any country deemed high-risk to apply for a visa, a hurdle that involves an interview at an American embassy or consulate (soldiers or government officials from allied nations are exempted). In parallel, the Department of Homeland Security (DHS) has moved to tweak the ESTA system to ask about previous travel to high-risk countries. The Senate bill would require ESTA applicants to submit fingerprints and photographs.

Because not every foreign fighter will obligingly display a visa stamp for Syria in their passports, the various proposals from Congress and the government put pressure on visa waiver countries to do more to collect and share intelligence with America, or face suspension from the scheme. Potential rows lurk: European countries have been wrangling with America for years about what sort of passenger data may legitimately be collected and shared.

Some proposed changes are uncontroversial. American authorities want to bring forward a deadline for all visa waiver passengers to travel on passports with embedded electronic chips, carrying such biometric data as fingerprints and facial images. The DHS wants to expand the number of foreign airports which host American passport and customs officers, so that passengers and their luggage are screened before their flights even take off. A first wave of expansion is expected to involve airports in Belgium, Japan, Norway, the Netherlands, Spain, Sweden and Britain. Airlines which fail to check a passenger’s passport data could face much stiffer fines. The Senate wants all visa waiver countries to sign legal agreements protecting federal air marshals who “take action” on flights. That may prove trickier.

If tightening visa waiver rules has inspired cross-party unity, the same cannot be said for refugee admissions. Following reports that at least one Paris attacker arrived in Europe claiming to be a Syrian refugee, Republican presidential candidates, members of Congress and the governors of 30 states (most of them Republicans) have demanded that the federal government halt or severely restrict refugee arrivals from Syria and a range of war-torn countries, including Iraq, Libya, and Yemen. A bill that would, in effect, suspend refugee arrivals from Syria and Iraq recently passed the House with 242 Republican and 47 Democratic votes, though President Barack Obama is expected to veto it.

In the Senate, proposals to restrict refugee arrivals are entangled with the presidential race. Senator Ted Cruz of Texas, a Republican seeking the presidency, has written a bill to suspend refugee arrivals from countries in which IS or other foreign terrorists control substantial territory, and a second which would let governors bar refugees from their states. Federal officials retort that the refugee visa system is the single most arduous route to America, involving multiple screenings and interviews by intelligence agencies lasting as long as two years, so that terror groups have little incentive to use it when far easier routes exist. Another presidential hopeful, Senator Rand Paul of Kentucky, wants to stop citizens of dozens of terror-stricken countries from entering America, and would impose a 30-day waiting period on visa waiver applicants—unless they apply through a Global Entry scheme involving an in-person interview. The most draconian schemes will not pass the Senate. But one way or another, entering America is about to get harder.