We present a new reconstruction of surface air temperature and sea surface temperature for the Last Glacial Maximum. The method blends model fields and sparse proxy-based point estimates through a data assimilation approach. Our reconstruction updates that of Annan and Hargreaves (2013), using the full range of general circulation model (GCM) simulations which contributed to three generations of the PMIP database, three major compilations of gridded sea surface temperature (SST) and surface air temperature (SAT) estimates from proxy data, and an improved methodology based on an ensemble Kalman filter. Our reconstruction has a global annual mean surface air temperature anomaly of -4.5Â±0.9 .sup." C relative to the pre-industrial climate. This is slightly colder than the previous estimate of Annan and Hargreaves (2013), with an upwards revision on the uncertainty due to different methodological assumptions. It is, however, substantially less cold than the recent reconstruction of Tierney et al. (2020). We show that the main reason for this discrepancy is in the choice of prior. We recommend the use of the multi-model ensemble of opportunity as potentially offering a credible prior, but it is important that the range of models included in the PMIP ensembles represent the main sources of uncertainty as realistically and comprehensively as practicable if they are to be used in this way.