This paper presents reduced conditions for the constitutive parameters of lossy bi-anisotropic media. It is shown that only two separate dyadic conditions, in contrast to the previously reported four, will be necessary and sufficient to characterize a medium as lossy. For the gyrotropic bi-anisotropic case revisited, it is found that these media call for merely two scalar conditions for their constitutive parameters, in contrast to the nine (reducible to seven) conditions formulated previously. The reduced dyadic and scalar conditions will simplify analysis of the physical realizability and the valid range of parameter values for new composite media. (C) 2004 Wiley Periodicals, Inc.