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It has often been demonstrated that conventional 4-state turbo codes do not perform well in either the waterfall or error-rate flare regions due to poor inherent convergence and distance properties, especially for highly-punctured codes. This paper shows that the opposite can be true when carefully chosen data and parity puncture masks are used with matching puncture-constrained dithered relative prime (DRP) interleavers. With an interleaver length of K=223 (8-meg), it is shown that waterfalls within 0.1 dB of capacity are possible for code rates R≥2/3. Waterfall performance can also be traded for improved distance to achieve very low error-rate flares. With an interleaver length of K=214 = 16384, R=8/9, and 50% data puncturing, a packet error rate of 10-6 was achieved within 0.57 dB of the corresponding binary sphere packing bound without using a cleanup code.