Innovations in intra block copy (“BC”) prediction mode facilitate intra BC prediction that is more effective in terms of rate-distortion performance and/or computational efficiency of encoding and decoding. For example, some of the innovations provide ways to select block vector (“BV”) values more effectively. Other innovations provide ways to encode/decode BV values more efficiently. Still other innovations address how to perform in-loop deblock filtering when a block has intra BC prediction mode, or address how to perform intra BC prediction when constrained intra prediction is enabled.