New intra angular prediction modes and methods for decoding are offered for providing greater accuracy when processing predictions of digital video data blocks. One new method considers predicting a current prediction sample by taking the linear interpolation of two previously reconstructed reference samples that lay along a common angular line. Another new method offers a method for making previously unavailable samples from a neighboring block available as reference samples when predicting a current prediction sample. Another new method considers a new combined intra prediction mode that utilizes a local mean to predict a current prediction sample. And a new decoding method offers to rearrange the order in which video data blocks are predicted based on the intra prediction mode used for predicting the video data blocks.