We describe a mechanism for approximate adaptive coding that makes use of deferred probability update to obtain good throughput rates with no buffering of symbols from the input message. Our proposed mechanism makes use of a novel code calculation process that allows an approximate code for a message of m symbols to be calculated in O(log m) time, improving upon previous methods. We also give analysis that bounds both the total computation time required to encode a message using the approximate code and the inefficiency of the resulting codeword set. Finally, experimental results are given that highlight the role the new method might play in a practical compression system. The current work builds upon two earlier papers. We previously described a mechanism for efficiently calculating a minimum-redundancy code for an alphabet in which there are many symbols with the same frequency of occurrence. We impose a modest amount of additional discipline upon the input frequencies, and show how the calculation of codewords can be performed in time and space logarithmic in the length of the message. The second area we have previously examined is the process of manipulating a code to actually perform compression. We examined mechanisms for encoding and decoding a prefix code that avoid any need for explicit enumeration of the source codewords. This means that we are free to change the source codewords at will during a message without incurring the additional cost of completely recalculating an n entry codebook.