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<p>Over the last decade, advanced statistical inference and machine learning have been used to fill the gaps in sparse surface ocean <span class="inline-formula">CO₂</span> measurements (Rödenbeck et al., 2015). The estimates from these methods have been used to constrain seasonal, interannual and decadal variability in sea–air <span class="inline-formula">CO₂</span> fluxes and the drivers of these changes (Landschützer et al., 2015, 2016; Gregor et al., 2018). However, it is also becoming clear that these methods are converging towards a common bias and root mean square error (RMSE) boundary: “the wall”, which suggests that <span class="inline-formula"><i>p</i>CO₂</span> estimates are now limited by both data gaps and scale-sensitive observations. Here, we analyse this problem by introducing a new gap-filling method, an ensemble average of six machine-learning models (CSIR-ML6 version 2019a, Council for Scientific and Industrial Research – Machine Learning ensemble with Six members), where each model is constructed with a two-step clustering-regression approach. The ensemble average is then statistically compared to well-established methods. The ensemble average, CSIR-ML6, has an RMSE of 17.16&thinsp;<span class="inline-formula">µ</span>atm and bias of 0.89&thinsp;<span class="inline-formula">µ</span>atm when compared to a test dataset kept separate from training procedures. However, when validating our estimates with independent datasets, we find that our method improves only incrementally on other gap-filling methods. We investigate the differences between the methods to understand the extent of the limitations of gap-filling estimates of <span class="inline-formula"><i>p</i>CO₂</span>. We show that disagreement between methods in the South Atlantic, southeastern Pacific and parts of the Southern Ocean is too large to interpret the interannual variability with confidence. We conclude that improvements in surface ocean <span class="inline-formula"><i>p</i>CO₂</span> estimates will likely be incremental with the optimisation of gap-filling methods by (1) the inclusion of additional clustering and regression variables (e.g. eddy kinetic energy), (2) increasing the sampling resolution and (3) successfully incorporating <span class="inline-formula"><i>p</i>CO₂</span> estimates from alternate platforms (e.g. floats, gliders) into existing machine-learning approaches.</p>