The unsteady, compressible, thin-layer Navier-Stokes equations are used to numerically study the passive control of steady and unsteady supersonic asymmetric flows around circular and noncircular cones. The main computational scheme of the present study is an implicit upwind, flux-difference splitting, finite-volume scheme. Passive control of flow asymmetry is studied by using a vertical fin in the leeward plane of geometric symmetry and side strakes with and without thickness at different orientations. The study focuses on circular-section cones since they are the most likely section-shapes for strong flow asymmetry. Side-strake passive control is shown to be more efficient and practical than vertical-fin passive control.