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We present an iterative approach to constructing pseudorandom generators, based on the repeated application of mild pseudorandom restrictions. We use this template to construct pseudorandom generators for combinatorial rectangles and read-once CNFs and a hitting set generator for width-3 branching programs, all of which achieve near-optimal seed-length even in the low-error regime: We get seed-lengthÕ(log(n/ε)) for error ε. Previously, only constructions with seed-length O(log 3/2 n) or O(log 2doi:10.1109/focs.2012.77 dblp:conf/focs/GopalanMRTV12 fatcat:4juxxydijne27bthnzi4crifg4