We extend the ideas of the perfect lens recently proposed [J.B. Pendry, Phys. Rev. Lett. 85, 3966 (2000)] to an alternative structure. We show that a slab of a medium with negative refractive index bounded by media of different positive refractive index also amplifies evanescent waves and can act as a near-perfect lens. We examine the role of the surface states in the amplification of the evanescent waves. The image resolution obtained by this asymmetric lens is more robust against the effects of absorption in the lens. In particular, we study the case of a slab of silver, which has a negative dielectric constant, with air on one side and other media such as glass or GaAs on the other side as an ‘asymmetric’ lossy near-perfect lens for p-polarized waves. It is found that retardation has an adverse effect on the imaging due to the positive magnetic permeability of silver, but we conclude that subwavelength image resolution is possible in spite of it.