Tom, thanks for the suggestion.
I have a birth extract of Kazimieras Mockunas (my grandfather) listing his parents and stating that he was born in Aukstuoliai village near Krincinas on 7 March 1877. He subequently moved away from that area and died in Kaunas in 1920. I have no other information on his parents. It is worth noting that Mockunas is not an uncommon surname in the Krincinas area, with several families represented in the local cemetery and in parish records.