Predictions of 21st century climate by different atmosphere-ocean general circulation models depend on the sensitivities of the models to external radiative forcing and on their rates of heat uptake by the deep ocean. This study constrains these properties by comparing radiosonde-based observations of temperature trends in the free troposphere and lower stratosphere with corresponding simulations of a fast, flexible climate model, using objective techniques based on optimal fingerprinting. Parameter choices corresponding either to low sensitivity, or to high sensitivity combined with slow oceanic heat uptake are rejected provided the variability estimates used from the HadCM2 control run are correct. Nevertheless, the range of acceptable values is significantly wider than that usually quoted. The IPCC's range of possible sensitivities, 1.5 to 4.5 K, corresponds at best to only an 80% confidence interval. Therefore, climate change projections based on current general circulation models do not span the range of possibilities consistent with the recent climate record. ¿ 2000 American Geophysical Union