LEGISLATIVE ping-pong continues between the two houses of Parliament over the bill allowing Theresa May to invoke Article 50 of the EU treaty, which will kick off the Brexit process. The prime minister hopes to persuade the Commons next week to reject two amendments made by the Lords, so that the bill can become law shortly afterwards. Yet many Tory MPs sympathise with at least one of those amendments, to instruct the government to guarantee the right to remain of over 3m EU nationals resident in Britain. The bipartisan Commons Brexit committee has just unanimously endorsed this suggestion.

Mrs May has long claimed that she too would like to do it. But last summer she declared that she could not without getting a reciprocal guarantee for the 1m or so Britons resident in other EU countries. Many of these feel neglected by their home government; most also support a unilateral guarantee for EU nationals. But some other EU countries say they cannot act until the Brexit negotiations begin. The impasse has created uncertainty and much anguish on both sides of the Channel.

In practice everyone agrees that almost all residents will be allowed to remain. Two-thirds of the 3m-plus EU nationals will have been in Britain for five years before Brexit, so they should qualify automatically. The bigger concern is the bureaucracy involved. A first problem is lack of information. Britain has no identity cards, no register of EU nationals and no checks on who comes and goes. The official numbers (see chart) are estimates that may well understate the true figures.

A second issue is the cut-off point for EU nationals who want to stay. Some have proposed June 23rd 2016, the date of the referendum, but this has no basis in law. Others are arguing for when Britain actually leaves, probably in March 2019, but that could encourage a last-minute surge. A report in December from British Future, a think-tank, floated a compromise of the day when Mrs May triggers Article 50 later this month.

Third and most problematic is the administrative burden of securing permanent residence, a necessary step towards citizenship. Last autumn Oxford’s Migration Observatory noted that, at current rates, it would take 140 years to process all those eligible. In the six months since the referendum the number applying rose to over 135,000. Many more are to come. The Home Office does not have enough staff to cope. Yet despite this it has tightened rather than relaxed the rules recently, says Colin Yeo, a specialist migration barrister.

Applicants must pay £65 ($80) and fill in an 85-page form (similar forms run to just two or three pages in Ireland and France). Many need legal help, as well as evidence of utility bills, payslips and all outward travel for five years. The process can take six months, during which time the Home Office keeps applicants’ passports. More bizarrely, any applicant who has been economically inactive must have had comprehensive sickness insurance, even though EU citizens have a right to use the National Health Service.

Sunder Katwala, director of British Future, says the proportion of applications being rejected because of such complexities is 30%. He reckons this would fall and the process speed up if those in work could bypass the Home Office and ask local-authority nationality-checkers to use income-tax data to confirm their status. He also suggests dumping the rule about sickness insurance. Yet the Home Office is a suspicious place that frets about ever being seen to let in even one illegal immigrant. Hard-luck stories and litigation lie ahead.

And this is all before, fourth, a new migration regime is put in place. The Commons Brexit committee suggests that EU citizens should be given preferential treatment. With industries such as agriculture and hospitality dependent on them, that may be sensible. Yet drawing up a system, getting employers and landlords to police it and persuading other EU countries to work with it will be hard—and could affect how long it takes to agree to let residents stay where they are. As Mrs May prepares to invoke Article 50, she must sometimes wonder if it would have been wiser to offer a unilateral guarantee to EU residents months ago, earning goodwill all round.