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The abundance distribution in the ejecta of the peculiar slowly declining Type Ia supernova (SN Ia) SN 1999aa is obtained by modelling a time series of optical spectra. Similar to SN 1991T, SN 1999aa was characterized by early-time spectra dominated by Fe iii features and a weak Si ii 6355 Å line, but it exhibited a high-velocity Ca ii H&K line and morphed into a spectroscopically normal SN Ia earlier. Three explosion models are investigated, yielding comparable fits. The innermost layers are dominated by ∼0.3 M⊙ of neutron-rich stable iron-group elements, mostly stable iron. Above that central region lies a 56Ni-dominated shell, extending to $v \approx 11\, 000$–$12\, 000$ km s−1, with mass ∼0.65 M⊙. These inner layers are therefore similar to those of normal SNe Ia. However, the outer layers exhibit composition peculiarities similar to those of SN 1991T: The intermediate-mass elements shell is very thin, containing only ∼0.2 M⊙, and is sharply separated from an outer oxygen-dominated shell, which includes ∼0.22 M⊙. These results imply that burning suddenly stopped in SN 1999aa. This is a feature SN 1999aa shares with SN 1991T, and explains the peculiarities of both SNe, which are quite similar in nature apart from the different luminosities. The spectroscopic path from normal to SN 1991T-like SNe Ia cannot be explained solely by a temperature sequence. It also involves composition layering differences, suggesting variations in the progenitor density structure or in the explosion parameters.