In a recent work, Andrews gave a definition of combinatorial objects which he called singular overpartitions and proved that these singular overpartitions, which depend on two parameters k and i, can be enumerated by the function $$\overline{C}_{k,i}(n) $$ C ¯ k , i ( n ) which denotes the number of overpartitions of n in which no part is divisible by k and only parts $$\equiv \pm i \ (\mathrm{mod}\ k)$$ ≡ ± i ( mod k ) may be overlined. Andrews, Chen, Hirschhorn and Sellers, and Ahmed and Baruah discovered numerous congruences modulo 2, 3, 4, 8, and 9 for $$\overline{C}_{3,1}(n)$$ C ¯ 3 , 1 ( n ) . In this paper, we prove a number of congruences modulo 16, 32, and 64 for $$\overline{C}_{3,1}(n)$$ C ¯ 3 , 1 ( n ) .