This paper proposes novel interleaver and accumulator structures for systematic, regular repeat-accumulate (RA) codes. It is well known that such codes are amenable to iterative (sum-product) decoding on the Tanner graph of the code, yet are as readily encodable as turbo codes. In this paper, interleavers for RA codes are designed using combinatorial techniques, as a basis for deterministic interleaver constructions, yielding RA codes whose Tanner graphs are free of 4-cycles. Further, a generalized RA code accumulator structure is proposed, leading to codes, termed w3RA codes, whose parity-check matrices have many fewer weight-2 columns than conventional RA codes. The w3RA codes retain the low-complexity encoding of conventional RA codes and exhibit improved error-floor performance.