Catholic unionists are, according to the commentator Fionnoula O'Connor, like unicorns - much talked about, but never seen.
Are they really hidden in the forest waiting to be tempted into the DUP, as Peter Robinson hopes? Or just a legend, as Ms O'Connor and the nationalist parties suspect?
It is a pressing question, because the Catholic proportion of the population is slowly, but steadily increasing.
In February, the Community Relations Council reworked government statistics to demonstrate that Catholics are already the majority community under the age of 35.
On December 11, we will have new census data which, some suspect, may show Catholics edging into the majority overall.
This was a nightmare scenario for Ulster unionism's founding fathers. The border was drawn and politics were conducted for 50 years with a view to maintaining the Catholic community as a manageable minority.
It was assumed that, if the sectarian balance tilted, Irish unity would follow. Some statistics bear that out - the combined votes of nationalist parties rises roughly in line with the broader Catholic population.
The catch is that, when asked if they wanted a united Ireland, there has always been a substantial and rising group of Catholics who would prefer to stay in the UK.
It was never less than 20%, even under unionist majority rule. Since powersharing, surveys like Northern Ireland Life and Times (NILT) and the Belfast Telegraph/LucidTalk poll last May, have shown that most Catholics prefer to stay in the UK. So wanting to stay in the UK doesn't mean voting unionist if you are a Catholic. It is more likely to be a rational decision based on economic and lifestyle choices.
Northern Ireland is no longer such a cold house for Catholics - symbols of Irish identity, such as the Irish language and the GAA, now have an honoured place, mainly Catholic parties share power, with an effective veto on many decisions.
There is entrenched equality legislation and underpinning it all is a subvention to Britain which the Republic, with its smaller tax-base, couldn't match.
NILT found that only 8% of Catholics thought of themselves as British, compared to 58% Irish and 25% Northern Irish.
Not many Catholic hearts would be warmed by the sea of union flags which made Mr Robinson's televised speech look like last night at the Proms. Few would join the cheer that went up when funding for the Orange Order was mentioned, or laugh along with Sammy Wilson's barbed humour.
There is a nervousness of a movement like the DUP gaining full control and cultural cringe at its trappings.
Faced with the choice, most Catholic voters will continue to back parties like Sinn Fein and the SDLP to act as a counterbalance and safeguard against unionist domination.
They might feel comfortable with the Union and support it in a poll, or in a referendum, but supporting unionist parties is a step too far.
For unionism to tap into a Catholic support-base, it would need a cultural audit to strip out any sectarian trappings and a more civic message.
In the legend, only a virgin, pure of body and mind, could catch a unicorn.