Armagh have been handed a difficult opening Football qualifier assignment against Laois at O’Moore Park.
Also on the weekend of 18-19 June, Derry will be at home to losers of the Leinster tie between Louth and Meath.
After their hammering by Monaghan on Sunday, Down will be at home to Longford on the weekend of 25-26 June.
Antrim will be at home to Limerick on the same weekend with the losers of the Fermanagh v Donegal Ulster tie facing Wexford away.
Armagh, comfortably beaten by Cavan in the Ulster quarter-finals nine days ago, lost at home against Laois in the Football League in early February.
After their home humiliation by Tyrone, Derry are unlikely to have it easy against either Louth or Meath at Celtic Park.
Louth won this year’s Division Four league title while Meath are invariably difficulty opponents in championship football.
Down face the task of regrouping from their mauling by Monaghan against Longford, who defeated Derry at Celtic Park in the qualifiers two years ago.
Longford narrowly missed out on securing promotion to Division Two of the League after winning four of their seven Division Three games so the Pairc Esler tie may be no easy task for the shell-shocked Mournemen.
After their promotion from Division Four in the Spring, Antrim should be capable of beating a Limerick team that dropped down to the final tier after only earning one point in Division Three.
The losers of this weekend’s Donegal v Fermanagh Ulster tie, meanwhile, should be good enough to account for a Wexford team that was unable to get out of Division Four this year.
All-Ireland SFC Qualifiers draw
Round 1A – 18-19 June
Laois v Armagh
Carlow v Wicklow
Derry v Louth or Meath
Leitrim v Waterford
Round 1B – 25-26 June
Down v Longford
Antrim v Leitrim
Offaly or Westmeath v London
Wexford v Fermanagh or Donegal