  We consider the C*-algebras O_2^q and A_2^q generated, respectively, by
isometries s_1, s_2 satisfying the relation s_1^* s_2 = q s_2 s_1^* with |q| <
1 (the deformed Cuntz relation), and by isometries s_1, s_2 satisfying the
relation s_2 s_1 = q s_1 s_2 with |q| = 1. We show that O_2^q is isomorphic to
the Cuntz-Toeplitz C*-algebra O_2^0 for any |q| < 1. We further prove that
A_2^{q_1} is isomorphic to A_2^{q_2} if and only if either q_1 = q_2 or q_1 =
complex conjugate of q_2. In the second part of our paper, we discuss the
complexity of the representation theory of A_2^q. We show that A_2^q is *-wild
for any q in the circle |q| = 1, and hence that A_2^q is not nuclear for any q
in the circle.
