  We consider the connected-sum method of constructing compact Riemannian
7-manifolds with holonomy G_2 developed in math.DG/0012189. The method requires
pairs of projective complex threefolds endowed with anticanonical K3 divisors,
the latter `matching' via a certain non-holomorphic map. Suitable examples of
threefolds were previously obtained in math.DG/0012189 by blowing up curves in
Fano threefolds.
  In this paper, we give further suitable algebraic threefolds using theory of
K3 surfaces with non-symplectic involution due to Nikulin. These threefolds are
not obtainable from Fano threefolds, as above, and admit matching pairs leading
to topologically new examples of compact irreducible G_2-manifolds. `Geography'
of the values of Betti numbers b^2,b^3 for the new (and previously known)
examples of compact irreducible G_2 manifolds is also discussed.
