A review of the referendum on blasphemy has recommended that similar votes in future should be staged alongside elections.
The Referendum Commission has noted that there was "very little public debate" about the idea of removing the offence of blasphemy from the Constitution. It passed with a majority of 65pc.
Turnout was 43.79pc - but the commission put this down to the fact the referendum was held on the same day as the presidential election.
Housing Minister Eoghan Murphy briefed colleagues on the commission's review at a Cabinet meeting earlier this week.
The commission advised the Government that future referendums "on which a high level of public debate is not anticipated should be put to the people either at the same time as an election, or at the same time as another matter is being put to the people, to ensure strong voter turnout".
This could have implications for the next referendum planned by the Government which relates to giving a vote in the presidential election to members of the diaspora. Taoiseach Leo Varadkar has indicated he hopes to stage the poll in October.
Last week's referendum on divorce also received very little public debate.
However, turnout was 50.83pc. It passed with a massive 82pc majority.