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Let p be the 1 to 0 bit error probability and h(p)=-p log2 p-(1-p) log2 (1-p). The capacity of the Z-channel is given by CZ=log2 (1+(1-p)pp(1-p)/). For small p, it is shown that CZ≈1-(1/2)h(p) (vs., CBS(p)=1-h(p) for the binary symmetric channel). Coding schemes are also given that almost achieve the Z-channel capacity.