It's pretty much head-to-head up at Stormont this summer as Peter Robinson and Martin McGuinness attempt to sweat down the remaining differences between the Democratic Unionists and Sinn Fein before sittings resume in the autumn.

The idea of bringing the Alliance party into the executive to handle policing is looking increasingly attractive. It could be the missing piece in a jigsaw of trade-offs, including the continued role of the IRA army council, the future of the Maze, the replacement of the 11-plus exam and the regulation of the Orange parades.

One of the problems facing Robinson is that, during the Chuckle Brothers era, Ian Paisley long-fingered all these difficult decisions. He and McGuinness concentrated on creating a feelgood factor at home and abroad, and didn't agree on many practical measures. Tough choices were avoided. So when the two of them set out to appoint a victims' commissioner, they ended up appointing all four candidates they had shortlisted rather than make a choice.

Gerry Adams has attempted to call a halt to the prevarication by hinting that, as Sinn Fein's nominating officer, he may pull the plug on Stormont if more substantive agreement is not reached on difficult issues.No one is quite sure if he is serious, but Adams has certainly succeeded in injecting some urgency into the process.

Under the St Andrews agreement, a target date of May was set by the two governments for devolution of policing and justice, but the DUP was never signed up for that. Nigel Dodds, now deputy leader, suggested last year that this question might best be left for a generation. Robinson hinted at a radical solution at a legal conference last Monday.

“Do we wait, potentially for years, perhaps for a generation, until the necessary level of support is reached for such options to gain widespread public confidence? Or do we search for another basis that may be able to command confidence in the community?”

Really, he needs to get things moving by September. If the decision drifts into another year, then it becomes an issue in next June's European elections. The DUP needs to oust Jim Allister, its former MEP, but if the issue isn't resolved he will be able to exploit fears that Robinson is prepared to hand a policing concession to Sinn Fein.

The easiest solution is to allow policing, and perhaps justice, to be shared by the two junior ministers in the Office of the First Minister and Deputy First Minister (OFM/DFM), an administrative behemoth with nearly as many staff as the White House and more than Downing Street. There are already 14 ministers there so, superficially, it avoids having to appoint another one.

The problem is that Gerry Kelly, Sinn Fein's junior minister in OFM/DFM, has done time for bombing the Old Bailey, the seat of British justice. Kelly has been a conscientious minister and has played a useful role in damping down trouble in north Belfast, but giving him a say in the criminal justice system would outrage the DUP's grass-roots. It would also be a gift to Allister. But then Sinn Fein is not going to allow Jeffrey Donaldson, a former part-time member of the army, to take charge while Kelly is excluded.

Another solution would be to run d'Hondt, the mathematical formula under which parties take turns to pick ministers. But there would be no guarantees about which party would pick what ministry, and negotiating a gentleman's agreement might take months. Bringing in the SDLP, which would mathematically be entitled to the next minister, or the UUP, would upset the nationalist/unionist balance of power on the executive.

As they attempt to square the circle, DUP and Sinn Fein negotiators are being pushed back to a solution used by direct-rule ministers in the past - bring in the Alliance party for the jobs that the nationalists and unionists don't trust each other to do.

Alliance is a creature so useful that if it didn't exist it would have to be invented. In some ways the party, which is linked to the Progressive Democrats in the republic and the Liberal Democrats in Britain, acts as Northern Ireland's conscience - a coalition of reasonable, middle-of-the-road folk united around an agenda which is liberal, pragmatic and non-sectarian.

While the other parties in the executive are designated nationalist or unionist for voting purposes, Alliance stands outside the sectarian blocks. Its seven MLAs share the designation “others” with the solitary Green member and Kieran Deeny, the hospital campaigner from Tyrone.

If these nine were allowed to form a party for assembly purposes then they, and not the SDLP, would mathematically be entitled to the next minister. But that would require new legislation at Westminster because the Justice and Security (Northern Ireland) Act 2007 specifies that the justice and policing minister must come from one of the two largest designations, currently unionist and nationalist. There is no doubt that Shaun Woodward, the secretary of state, and Gordon Brown would rush through such legislation if required.

There are plenty of examples of Alliance pulling the irons out of the fire before. When the British and Irish governments wanted to pick a Northern Ireland representative for the decommissioning body, it was obvious that they couldn't pick a nationalist or unionist, so their choice was Lord Alderdice, a former Alliance leader, and he met general acceptance. He had been speaker of an earlier assembly, as had his party colleague Eileen Bell, at a period when agreement could not be reached between nationalists and unionists.

The late Bob Cooper, another Alliance stalwart, was chosen to head the Fair Employment Agency, the first statutory body set up to tackle religious and political discrimination. David Cook, a solicitor and former leading Alliance party member, was put in charge of the Police Authority when the first policing reforms were being pushed through.

Across the province, Alliance has used its votes on local councils to ensure that posts are rotated between nationalists and unionists. In the Trimble/Mallon assembly, members of Alliance, along with the Women's Coalition, were persuaded to redesignate as unionist or nationalist to ensure that the institution survived a crisis.

If policing and justice are to be devolved, it is difficult to see agreement being reached to give the ministry to anyone other than Alliance. Anna Lo, the first Chinese-born person to be elected to any legislative assembly in Europe, would not only be an able minister but a symbolically important choice. Other Alliance figures such as Stephen Farry, Naomi Long or David Ford, the party leader and nominating officer, are also well suited for ministerial responsibility.

Ford was sounded out about the ministry by Peter Hain during the St Andrews negotiations. Hain suggested that an Alliance policing and justice minister be included in the OFM/DFM, appointed by the DUP and Sinn Fein, but with no voting rights.

This second-class status was turned down and would be rejected again. Instead, Alliance is likely to seek full voting rights and to use them to press for an increased role for parties who, like themselves and the Greens, appeal for votes outside the tribal headcount which has turned every election since the foundation of the state into an unofficial border poll.

They may well be working with the grain of history. Many Northern politicians report that as peace and security settles down but the credit crunch bites, they are more often asked what they will do about jobs and services than about flags, emblems and the border.

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