We study the interaction between a small, magnetized asteroid and the solar wind (SW) in the ''submagnetospheric'' regime, in which the asteroid's magnetic field is too small to establish either a cavity, from which the solar wind is excluded, or a magnetic tail. The interaction is described in terms of dispersive anisotropic MHD waves which are generated by a point-like asteroid and these are phase-standing in its rest frame. The fast-mode whistler waves give rise to a bow wave/wake wave, the characteristics of which are controlled by the direction of the interplanetary magnetic field (IMF) relative to the SW flow direction and by the orientation of the asteroids magnetic moment. Both the fluid-oriented Hall-MHD model and the fully kinetic dielectric tensor approach are employed to describe the SW plasma. Typical features of the whistler bow wave (e.g., the relevant wavelengths) can be modeled as 2D by treating the obstacle as a line dipole. We find that pronounced, upstream-directed wave activity occurs in cases where the IMF has a large component in the direction of the flow. Three-dimensional calculations demonstrate that the IMF acts as a guide for the propagation of magnetic field perturbations and also that a magnetic moment of least 10(12) A m(2) is required to produce observable (i.e., delta B/B greater than or equal to 0.1) perturbations in the IMF, at a distance of approximately 1000 ion from the asteroid. (C) 1997 Academic Press.