The only statement that Bernhard's second wife (or mistress) was Vladimirovna, daughter of Vladimir Sviatoslavich, cites a 1722 source that doesn't actually say that, so Cawley assumes it is not true. However, it is known that she was Slav, from a 1057 source.
Her son Otto's birth is estimated as about 1040 because he was described as an adolescent when he was killed in battle 26 Jun 1057.
↑ Birth estimated based on the estimated birth year of her son Otto (1040) and the possibility that she was the daughter of Vladimir, who died in 1015.
