A continuous record of direct total solar irradiance (TSI) observations began with a series of satellite experiments in 1978. This record requires comparisons of overlapping satellite observations with adequate relative precisions to provide useful long term TSI trend information. Herein we briefly review the active cavity radiometer irradiance monitor physikalisch-meteorologisches observatorium davos (ACRIM-PMOD) TSI composite controversy regarding how the total solar irradiance (TSI) has evolved since 1978 and about whether TSI significantly increased or slightly decreased from 1980 to 2000. The main question is whether TSI increased or decreased during the so-called ACRIM-gap period from 1989 to 1992. There is significant discrepancy between TSI proxy models and observations before and after the gap, which requires a careful revisit of the data analysis and modeling performed during the ACRIM-gap period. In this study, we use three recently proposed TSI proxy models that do not present any TSI increase during the ACRIM-gap, and show that they agree with the TSI data only from 1996 to 2016. However, these same models significantly diverge from the observations from 1981 and 1996. Thus, the scaling errors must be different between the two periods, which suggests errors in these models. By adjusting the TSI proxy models to agree with the data patterns before and after the ACRIM-gap, we found that these models miss a slowly varying TSI component. The adjusted models suggest that the quiet solar luminosity increased from the 1986 to the 1996 TSI minimum by about 0.45 W/m2 reaching a peak near 2000 and decreased by about 0.15 W/m2 from the 1996 to the 2008 TSI cycle minimum. This pattern is found to be compatible with the ACRIM TSI composite and confirms the ACRIM TSI increasing trend from 1980 to 2000, followed by a long-term decreasing trend since.