The variety pO consists of those algebras (L; ∧, ∨, f,*, 0,1) of type (2,2,1,1,0,0) where (L; ∧, ∨, f, 0,1) is an Ockham algebra, (Z; ∧, ∨,*, 0,1) is a p-algebra, and the unary operations f and * commute. We describe completely the structure of the subdirectly irreducible algebras that belong to the subclass pK1,1, characterised by the property f3 = f.