Adaptive variable-length codes associate a variable-length codeword to the symbol being encoded depending on the previous symbols in the input string. This class of codes has been recently presented in [Dragos Trinca, arXiv:cs.DS/0505007] as a new class of non-standard variable-length codes. New algorithms for data compression, based on adaptive variable-length codes of order one and Huffman's algorithm, have been recently presented in [Dragos Trinca, ITCC 2004]. In this paper, we extend the work done so far by the following contributions: first, we propose an improved generalization of these algorithms, called EAHn. Second, we compute the entropy bounds for EAHn, using the well-known bounds for Huffman's algorithm. Third, we discuss implementation details and give reports of experimental results obtained on some well-known corpora. Finally, we describe a parallel version of EAHn using the PRAM model of computation.