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We consider the nearest-neighbor simple random walk on ℤ, ≥2, driven by a field of bounded random conductances ∈[0, 1]. The conductance law is i.i.d. subject to the condition that the probability of >0 exceeds the threshold for bond percolation on ℤ. For environments in which the origin is connected to infinity by bonds with positive conductances, we study the decay of the 2-step return probability ${𝖯}_{\omega }^{2n}(0,0)$. We prove that ${𝖯}_{\omega }^{2n}(0,0)$ is bounded by a random constant times ...