The string matching encoders were proposed about 20 years ago, when the lz77 and lz78 were introduced. They became extremely popular because of the relationship between their low complexity and their good performance. Although these encoders are universal, that is, their compression rates converge to the source entropy, it was shown, recently, that those rates do not converge as fast as possible, even for the class of memoryless source. The redundancy of an unversal encoder C, denoted by Rc, measures how fast the compression rate converge to the entropy. In the class of Finite State Machine (FSM) source, while the best result of the string matching encoders is O 1/ {log n}, there are encoders which achieve a redundancy of O {log n}/n. Therefore, the string matching encoders are not optimal. Even though optimal encoders are known, in general, those encoders have a high complexity and are not useful in practice. Considering the class of string matching encoders, the lz78 has one of the best results over the class of FSM source. In fact, there is no encoder based on the string matching, which archives a better redundancy. This work makes use of the lz78 encoder to propose new techniques to improve the performance of sting matching encoders over the class of FSM. These techniques bring up new versions of the lz78. For the class of FSM, the redundancies of this versions are stablished. These versions are used to compress data files, and their perfoermances are compared to the performances of older versions.