The possibility of using plasmonic and metamaterial covers to drastically reduce the total scattering cross section of spherical and cylindrical objects is discussed. While it is intuitively expected that increasing the physical size of an object may lead to an increase in its overall scattering cross section, here we see how a proper design of these lossless metamaterial covers near their plasma resonance may induce a dramatic drop in the scattering cross section, making these objects nearly “invisible” or “transparent” to an outside observer—a phenomenon with obvious applications for low-observability and noninvasive probe design. Physical insights into this phenomenon and some numerical results are provided.