Conventional intra-frame coding is performed in two steps. First, a block of pixels are predicted by copying previously reconstructed neighbor pixels of the block along an angular direction inside the block. Then, the prediction residual block is transform-coded with the well-known 2-D Discrete Cosine Transform (DCT). Recently, it has been shown that transforming the intra prediction residuals with the odd type-3 Discrete Sine Transform (ODST-3) along the prediction direction and the DCT along the perpendicular direction improves the compression performance. More recently, a recursive prediction approach has been proposed for intra prediction. In this paper, we show that combining the recursive intra prediction approach and the ODST-3/DCT transform improves overall intra-frame compression performance relative to using only one of these methods. We also show that this performance can be improved further by developing transforms specifically adapted to the prediction residuals of the recursive intra prediction approach.