This paper proposes a new construction of rate-adaptive coding schemes based on Low Density Parity Check (LDPC) codes for Slepian Wolf source coding. Unlike standard rate-adaptive source coding schemes, the code construction we propose is based on finite-length code design tools that permit to greatly improve the decoding performance at short to moderate length. In particular, our method permits to limit the number of short cycles in the codes at all rates of interest, and to avoid eliminating some source bits from the code constraints. The proposed method shows a performance improvement of up to an order of magnitude at almost all the considered rates compared to the standard LDPCA construction.