In this work, three techniques for enhancing various chaos-based joint compression and encryption (JCAE) schemes are proposed. They respectively improved the execution time, compression ratio, and estimation accuracy of three different chaos-based JCAE schemes. The first uses auxiliary data structures to significantly accelerate an existing chaos-based JCAE scheme. The second solves the problem of huge multidimensional lookup table overheads by sieving out a small number of important sub-tables. The third increases the accuracy of frequency distribution estimations, used for compressing streaming data, by weighting symbols in the plaintext stream according to their positions in the stream. Finally, two modified JCAE schemes leveraging the above three techniques are obtained, one applicable to static files and the other working for streaming data. Experimental results show that the proposed schemes do run faster and generate smaller files than existing JCAE schemes, which verified the effectiveness of the three newly proposed techniques.