In this paper we continue the study of Q-operators in the six-vertex model and its higher spin generalizations. In  we derived a new expression for the higher spin R-matrix associated with the affine quantum algebra Uq(sl(2)ˆ). Taking a special limit in this R-matrix we obtained new formulas for the Q-operators acting in the tensor product of representation spaces with arbitrary complex spin.Here we use a different strategy and construct Q-operators as integral operators with factorized kernels based on the original Baxter's method used in the solution of the eight-vertex model. We compare this approach with the method developed in  and find the explicit connection between two constructions. We also discuss a reduction to the case of finite-dimensional representations with (half-)integer spins.