Recently Jenei introduced a new structure called equality algebras which is inspired by ideas of BCK-algebras with meet. These algebras were generalized by Jenei and Kóródi to pseudo equality algebras which are aimed to find a connection with pseudo BCK-algebras with meet. We show that such pseudo equality algebras are an equality algebras. Therefore, we define a new type of algebras, called JK-algebras, which more precisely reflects the relation to pseudo BCK-algebras with meet in the sense of Kabziński and Wroński. We describe congruences via normal closed deductive systems, and we show that the variety of JK-algebras is subtractive, congruence distributive and congruence permutable.