The quality degradation of transmitted speech in current telephone systems due to the band limitation can be reduced by application of an enhancement system which generates "pseudo" wide-band speech from its telephone-band version. In this contribution, an extended classification approach is presented as a component of such an enhancement system. The incoming telephone-band signal is divided into the spectral envelope and the residual signal by means of an LPC-error-filter. The proposed method focuses on the enhancement of the spectral envelope. At this, an appropriate set of spectral wide-band envelopes is selected from a pre-trained codebook in two steps. In the first step a subset of proper wide-band envelopes is selected. This is then further reduced in the second step by means of a cost-function which takes account of the relationship between the wide-band envelopes of the subset and the resulting wide-band envelope of the classification procedure one time step earlier. Listening tests have shown that the extended classification is a proper approach to enhance the quality of the synthesized signal components.