Analyses are presented to show that water admitted to the drywell of a Mark I boiling water reactor can significantly attenuate radionuclide releases during severe reactor accidents. This attenuation can be achieved whether or t_ot water is able to prevent or delay failure of the drywell. Attenuation of releases of radioactive materials is achieved by the actions or"water pools maintained over core debris interacting with concrete in the drywell and by the actions of drywell sprays. A mechanistic model is formulated of the aerosol scrubbing by a water pool overlying core debris that is interacting with concrete. Eighteen uncertain features of the model are identified. A quantitative uncertainty analysis of the model is described. Cumulative probability distribution functions are developed at confidence levels of 50, 90, and 95 percent for the decontamination factors that can be achieved by water pools 30 and 50 cm deep with subcooling of 0, 2, 5, 10, 20, 30, 50, and 70°C. These distribution functions show with high confidence that the radionuclide emissions during core debris interactions with concrete can be reduced by a factor of 10 and perhaps by a factor in excess of 100 by shallow, subcooled water pools. It is argued that similar decontamination factors would be realized even if core debris penetrated the Mark I liner and flowed into the reactor torus room. Features of spray systems in the drywells of Mark I containments are described. A mechanistic model is formulated of the aerosol scrubbing that can be achieved by drywell sprays. Nineteen uncertain features of the model are identified and quantities are defined to describe the uncertainty of these features. Ranges of values for uncertain quantities and distributions for values within these ranges are defined. A quantitative uncertainty analysis of the model is described. Cumulative probability distribution functions are developed at confidence levels of 50, 90 and 95 percent for the decontamination coefficient produced by sprays for water fluxes into the drywell of 0.002, 0.01 and 0.25 cm3/cm2-s. Rapid removal of aerosols by spray droplets can be expected with high con_,dence only for the highest water fluxes (-0.25 cm 3 H20/cm2-s). These high water fluxes are within the capabilities of spray systems in some Mark I drywells. At lower water fluxes, decontamination of the drywell atmosphere can be achieved if drywell failure is delayed and the leak rate following drywell failure is not large. Correlations of the results obtained in the uncertainty analyses of decontamination by water pools and by sprays are used in an example analysis of a hypothetical accident at a Mark I boiling water reactor.