We consider various forms of a process, which we call gluing, for combining two or more complementary quantum channel pairs (B,C) to form a composite. One type of gluing combines a perfect channel with a second channel to produce a generalized erasure channel pair (Bg,Cg). We consider two cases in which the second channel is (i) an amplitude-damping, or (ii) a phase-damping qubit channel; (ii) is the dephrasure channel of Leditzky et al. For both (i) and (ii), (Bg,Cg) depends on the damping parameter 0 ≤ p ≤ 1 and a parameter 0 ≤ λ ≤ 1 that characterizes the gluing process. In both cases we study Q(1)(Bg) and Q(1)(Cg), where Q(1)is the channel coherent information, and determine the regions in the (p, λ) plane where each is zero or positive, confirming previous results for (ii). A somewhat surprising result for which we lack any intuitive explanation is that Q(1)(Cg) is zero for λ ≤ 1/2 when p=0, but is strictly positive (though perhaps extremely small) for all values of λ > 0 when p is positive by even the smallest amount. In addition we study the nonadditivity of Q(1)(Bg) for two identical channels in parallel. It occurs in a well-defined region of the (p, λ) plane in case (i). In case (ii) we have extended previous results for the dephrasure channel without, however, identifying the full range of (p, λ) values where nonadditivity occurs. Again, an intuitive explanation is lacking.