Differences among total solar irradiance (TSI) estimates are most pronounced during the so-called “ACRIM Gap” of 1989–1991, when available satellite observations disagree in trend and no observations exist from satellites with on-board calibration. Different approaches to bias-correcting noisy satellite observations lead to discrepancies of up to 0.7 W/m² in the change in TSI during the Gap. Using a Bayesian hierarchical model for Total Solar Irradiance (BTSI), we jointly infer TSI during the ACRIM Gap from satellite observations and proxies of solar activity. In addition, BTSI yields estimates of noise and drift in satellite observations and calibration for proxy records. We find that TSI across the ACRIM Gap changes by only 0.01 W/m², with a 95% confidence interval of [-0.07, 0.09] W/m². Our results are consistent with the PMOD CPMDF and Community Consensus TSI reconstructions and inconsistent with the 0.7 W/m² trend reported in the ACRIM composite reconstruction. Constraints on the trend across the ACRIM Gap are primarily obtained through constraints on the drift in the Nimbus-7 satellite that are afforded by overlapping satellite and proxy observations.