This paper presents specific new techniques for coding of speech representations and a new general approach to coding for compression that directly utilizes the multidimensional nature of the input data. Many methods of speech analysis yield a two-dimensional (2-D) pattern, with time as one of the dimensions. Various such speech representations, and power spectrum sequences in particular, are shown here to be amenable to 2-D compression using specific models which take account of a large part of their structure in both dimensions. Newly developed techniques, multistep adaptive flux interpolation (MAFI) and multistep flow-based prediction (MFBP) are presented. These are able to code power spectral density (PSD) sequences of speech more completely and accurately than conventional methods. This is due to their ability to model nonstationary, but piecewise-continuous, signals, of which speech is a good example. Initially, MAFI and MFBP are applied in the time domain, then reapplied to the encoded data in the second dimension. This approach allows the coding algorithm to exploit redundancy in both dimensions, giving a significant improvement in the overall compression ratio. Furthermore, the compression may be reapplied several times. The data is further compressed with each application.