Till now, some Joint Fingerprinting and Decryption (JFD) schemes have been reported, while few works have been done to analyze their performances. In this paper, the security of the JFD scheme proposed by Kundur et al. is analyzed and improved. The analyses include the compliance with general compression codecs, the security against cryptographic attacks, the security in perception, the relationship between security and robustness, and the relationship between security and imperceptibility. Additionally, some means are proposed to improve the scheme's performances. The encryption in block based DCT is introduced to make it compliant with such compression codec as JPEG or MPEG2. The multi-key encryption is presented to improve the security against cryptographic attacks. The DC encryption is proposed to strengthen the perceptual security against ciphertext-only attacks. These analysis methods can also be used to evaluate some other JFD schemes, and are expected to provide valuable information to design JFD schemes.