Cryptography is one of the technological means to provide security to data being transmitted on information and communication systems. When it is necessary to securely transmit data in limited bandwidth, both compression and encryption must be performed. Researchers have combined compression and encryption together to reduce the overall processing time. In this paper, new partial encryption schemes are proposed to encrypt only part of the compressed image. Soft and hard threshold compression methods are used in the compression step and the Advanced Encryption Standard (AES) cipher is used for the encryption step. The effect of different threshold values on the performance of the proposed schemes are studied. The proposed partial encryption schemes are fast, secure, and do not reduce the compression performance of the underlying selected compression methods.