There exist two constructions of families of exotic monotone Lagrangian tori in complex projective spaces and products of spheres, namely the one by Chekanov and Schlenk and the one via the Lagrangian circle bundle construction of Biran. It was conjectured that these constructions give Hamiltonian isotopic tori. I will explain why this conjecture is true in the complex projective plane and the product of two two-dimensional spheres.