A hybrid PARAFAC and principal-component model of tongue configuration in vowel production is presented, using a corpus of German vowels in multiple consonant contexts (fleshpoint data for seven speakers at two speech rates from electromagnetic articulography). The PARAFAC approach is attractive for explicitly separating speaker-independent and speaker-dependent effects within a parsimonious linear model. However, it proved impossible to derive a PARAFAC solution of the complete dataset (estimated to require three factors) due to complexities introduced by the consonant contexts. Accordingly, the final model was derived in two stages. First, a two-factor PARAFAC model was extracted. This succeeded; the result was treated as the basic vowel model. Second, the PARAFAC model error was subjected to a separate principal-component analysis for each subject. This revealed a further articulatory component mainly involving tongue-blade activity associated with the flanking consonants. However, the subject-specific details of the mapping from raw fleshpoint coordinates to this component were too complex to be consistent with the PARAFAC framework. The final model explained over 90% of the variance and gave a succinct and physiologically plausible articulatory representation of the German vowel space.