We describe the dynamics of a class of MHD winds from Keplerian-rotating disks. In this model, all flow velocities are assumed to vary self-similarly with spherical radius r as υ(r, θ) ∝ r−1/2, with density varying as ρ(r, θ) ∝ r−q for arbitrary q. At large distances from the disk, the wind is explicitly required to become cylindrically collimated. We find that the asymptotic wind solution has power-law scalings of all flow variables in the cylindrical radius R = r sin θ, and q < 1 is necessary. We describe how the Alfvén criticality condition limits the space of energy and angular momentum parameters defining these wind solutions. We present an example of the run of density, velocity, and magnetic field for a full solution of the wind equations, and compare the properties of these cylindrically-collimated wind solutions to previous work.