This paper deals with the extension of a recent study of the infrared 1 Π → 1 Σ emission system of the YI molecule (1). Thanks to the extreme regularity of the structure, rotational analyses can be completed for the previous 3-1, 2-0, 1-0, 0-0 and 0-1 bands and extended to 11 more bands detected step by step from their synthetic spectra (owing to the extremely dense structure). A unique and consistent set of accurate rotational constants is derived for both states, up to the levels υ" = 7 and υ' = 4, from the reduction of 5772 line wavenumbers in the bands 3-1, 2-0, 1-0, 0-0. 0-1. 0-2, 1-3, 2-4, 2-5, 3-6 and 4-7, the υ-connected bands being fitted simultaneously. The 57 estimated constants allow to reproduce the observed spectra with typical weighted rms errors between 4 and 5 mK. When using these constants to generate the bands 2-1, 1-2, 3-3, 1-4 and 3-5, ~1300 lines can be picked out whose experimental positions relatively to the predicted ones correspond to quite equivalent rms errors with nearly normal distributions of the residuals, therefore ensuring the reliability of the analysis. Molecular constants at equilibrium are derived; improvments are significant, particularly for vibration. Franck-Condon factors and r-centroïds appropriate to RKR potential curves are given. The observed bands correspond to those which are predicted to be the strongest ones in each υ'-progression.