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tokens: to three and four for C nTh + C Th and C nTh + C Th + ( C )PL, respectively. In this article we reanalyzed three famous bright long GRBs (namely, GRBs 941017, 970111, and 990123) observed with BATSE on board the Compton Gamma Ray Observatory ( CGRO )—which was operating in low-Earth orbit from 1991 to 2000—in the context of the new paradigm to verify its consistency with these archival data. This article does not aim to be a full validation of the new model and relation, but rather to show that the results obtained with Fermi also hold with the data of other instruments too. It is a crucial step since it reduces the risk that instrumental calibration/systematic effects may account for the results. A comprehensive study of the new model and relation using an extensive sample of GRBs detected with multiple instruments is in progress, but it is out of the scope of the current paper. In Sections 2 and 3 we discuss the data selection criteria and our analysis methodology. In Section 4 we present our results. We will see how the view we had of those GRBs—which attracted a lot of attention in the scientific community—may be completely refreshed in the framework of the new model. 2. DATA SELECTION We focus this first article of a series on a limited sample of three famous bright long GRBs detected with BATSE. These GRBs are of particular interest because they have often been and still are cited to support or discard theoretical interpretations for GRB prompt emission. GRB 990123 was the first GRB to be simultaneously detected during its prompt phase in the γ -ray and optical bands (Akerlof et al. 1999 ). The prompt emission spectra of this burst in the keV–MeV energy range was considered to be adequately fitted to a single Band function (Briggs et al. 1999 ). A redshift estimate for the burst of 1.61 was reported by Kelson et al. ( 1999 ) and Hjorth et al. ( 1999 ). GRB 941017—which was also observed with EGRET on board CGRO —was the first burst of the pre- Fermi era for which a strong deviation at high energy from the Band function was reported (González et al. 2003 ). GRB 941017 was considered to be adequately fitted to a combination of a Band function fading with time and an additional PL remaining constant and incompatible with the synchrotron models. Unfortunately no redshift was measured for this GRB. Finally, we also analyzed GRB 970111 which was thought to be adequately fitted to a Band function but with positive values of at early times. The photometric redshift of this burst was estimated to be 0.2 z 1.4 based on its probable association with host galaxies at this redshift range (Gorosabel et al. 1998 ). Unfortunately, many fainter galaxies may lie in the same region of the sky and the association with the detected objects is not secure, which jeopardizes the validity of this photometric redshift. The light curves of GRBs 941017, 970111, and 990123 are presented in Figures 1 – 3 , respectively. Figure 1. GRB 941017 count light curves as