An extension of a regression-based methodology for constraining climate forecasts using a multi-thousand member ensemble of perturbed climate models is presented, using the multi-model CMIP-3 ensemble to estimate the systematic model uncertainty in the prediction, with the caveat that systematic biases common to all models are not accounted for. It is shown that previous methodologies for estimating the systematic uncertainty in predictions of climate sensitivity are dependent on arbitrary choices relating to ensemble sampling strategy. Using a constrained regression approach, a multivariate predictor may be derived based upon the mean climatic state of each ensemble member, but components of this predictor are excluded if they cannot be validated within the CMIP-3 ensemble. It is found that the application of the CMIP-3 constraint serves to decrease the upper bound of likelihood for climate sensitivity when compared with previous studies, with 10th and 90th percentiles of probability at 1.5 K and 4.3 K respectively.