Innovations in intra-picture prediction with multiple candidate reference lines available are described herein. For example, intra-picture prediction for a current block uses a non-adjacent reference line of sample values to predict the sample values of the current block. This can improve the effectiveness of the intra-picture prediction when the reference line of sample values that is adjacent the current block includes significant capture noise, significant quantization error, or significantly different values (compared to the current block) due to an occlusion. Innovations described herein include, but are not limited to, the following: intra-picture prediction with multiple candidate reference lines available; encoding/decoding of reference line indices using prediction; filtering of reference sample values; residue compensation; weighted prediction; mode-dependent padding to replace unavailable reference sample values; using in-loop-filtered reference sample values; encoder-side decisions for selecting reference lines; and post-filtering of predicted sample values.