Multifrequency Born inversion of the dielectric object is modified to include the lossy dielectric in a slightly lossy background medium. Two typical numerical examples of a circular and an L-shaped lossy dielectric cylinder are presented with their ranges of validity. By using the improved Born inversion, a permittivity contrast of 1-6 may be reconstructed but the range of conductivity is rather limited. (C) 1995 John Wiley & Sons, Inc.