Experiments have been carried out with models of free-to-rotate parallel and oblique plates fitted to a rigid section of circular cylinder to investigate the effect of plate length and oblique angle on the stability of this type of vortex-induced vibration (VIV) suppressor. Measurements of the dynamic response and trajectories of motion are presented for models with low mass and damping which are free to respond in the cross-flow and streamwise directions. It is shown that, depending on a combination of some geometric parameters, the devices might not be able to completely suppress VIV for the whole range of reduced velocities investigated. Plates with larger oblique angles turned to be less stable than parallel plates and induced high-amplitude vibrations for specific reduced velocities. Systems may present streamwise vibration due to strong flow separation and reattachment on the outer surface of plates with large oblique angles. Large angles may also increase drag. Experiments with a plain cylinder in the Reynolds number range from 3000 to 20,000 have been performed to serve as reference. Reduced velocity was varied between 2 and 13. Two-dimensional numerical simulation of static systems at Re = 10,000 revealed that complex and fully separated flow regimes exist for almost all investigated cases. There is a good chance that systems with such geometric characteristics will be unstable unless other structural parameters are positively verified.