A gap in the total solar irradiance (TSI) measurements between ACRIM-1 and ACRIM-2 led to the ongoing debate on the presence or not of a secular trend between the minima preceding cycles 22 (in 1986) and 23 (1996). It was recently proposed to use the SATIRE model of solar irradiance variations to bridge this gap. When doing this, it is important to use the appropriate SATIRE-based reconstruction, which we do here, employing a reconstruction based on magnetograms. The accuracy of this model on months to years timescales is significantly higher than that of a model developed for long-term reconstructions used by the ACRIM team for such an analysis. The constructed ‘mixed’ ACRIM — SATIRE composite shows no increase in the TSI from 1986 to 1996, in contrast to the ACRIM TSI composite.