Three-dimensional (3D) convection and segregation due to imperfect growth conditions, such as ampoule tilting and asymmetric heating, are common problems in vertical Bridgman crystal growth. How to suppress the 3D effects has been an important task for better growth control. To investigate the possibility of using steady ampoule rotation to damp the 3D flows, numerical simulation is conducted. It is found that the low-speed rotation (e.g., 10 RPM) can reduce significantly the 3D flows, but may result in larger radial segregation due to less dopant mixing, as well as rotational growth and melting. For weaker convection, which corresponds to a low-thermal-gradient or reduced-gravity growth, ampoule rotation is particularly effective. This is especially true in space, where the 3D flows and segregation induced by an arbitrary residual gravity can be significantly suppressed by only several RPM of ampoule rotation leading to a nearly diffusion-controlled growth. However, if the growth interface is not axisymmetric, which is often caused by an asymmetric heating, rotational segregation can be quite severe, even without the buoyancy convection.