Innovations in the area of prediction of block vector (“BV”) values improve encoding or decoding of blocks using intra block copy (“BC”) prediction. For example, some of the innovations relate to use of a default BV predictor with a non-zero value. Other innovations relate to use of a selected one of multiple BV predictor candidates for a current block. Still other innovations relate to use of a skip mode in which a current intra-BC-predicted block uses a predicted BV value.