Despite great progress in the coverage of ocean observing systems, two regions remain poorly monitored, the Arctic and the deep ocean below 2000 m, which is slightly over half of the ocean's volume. While significant trends in oceanic bottom water warming in recent decades can be discerned from repeat hydrographic surveys [Purkey and Johnson, 2010], they are too sparse to adequately quantify the deep ocean contribution to the present day sea level and ocean heat content budgets. However, deep ocean warming can be inferred from models or from complementary observations. Song and Colbert [2011] suggest that deep ocean warming below 700 m may have contributed 1.1 mm/yr to the global mean sea level rise (SLR), which is one-third of the rate of SLR (3.1 +/- 0.6 mm/yr) observed by altimetry over 1993-2008. This estimate is considerably larger than the long-term values from earlier hydrographic studies [e.g. Levitus et al., 2005], which find a trend of 0.07 +/- 0.1 mm/yr in the SLR for the depth range 700-3000 m during 1955-2003, and 0.09 +/- 0.06 mm/yr below 3000 m since the 1980s. While these estimates may be biased low because of inadequate deep-ocean sampling, recent sea level budget studies also suggest that only a small rate of deep warming is necessary for closure of the budget [e.g. Leuliette and Willis, 2011; Church et al., 2011]. Using a decade of altimetry, GRACE, and Argo observations, we present an estimate of the sea level budget and explore the use of the residuals of the budget to infer recent trends in deep ocean warming. With this method we find that during January 2005 to December 2013, warming in the ocean below 2000 m is contained to < 0.2 +/- 0.5 mm/yr. Crucial to constraining estimates of deep ocean warming are estimates of any drifts in the observations from the observing systems used. We also discuss a new system to compare altimetry and tide gauge observations to estimate drifts.