Problem of embedding message in steganography

i am doing my final year project on image steganography. Basically i am tranforming the image into frequency domain using Discrete Fourier Transform and then embedding the message bit by bit in the fourier coefficients. Finally, performing the Inverse fourier transformation to get back my original pixel values. For extraction of the message i am performing the DFT once again and then extract the bits.
The problem is that when i am embedding in the LSB of the fourier coefficients, then next time i do the fourier, i am getting slightly different values for which the intended bit i.e. LSB is changed. I have tried embedding the message bit in the higher bit also but that is also creating problem since sometimes even though the fourier coefficients are close, the change is getting reflected in the higher bit (eg 543 and 544 i am hiding the message in the 5th bit from LSB and that is getting changed)

Can anyone give me a new idea to do this for which the message can be extracted nicely ?