Individuals are becoming increasingly concerned with privacy. This curtails their willingness to share sensitive attributes like age, gender or personal preferences; yet firms largely rely upon customer data in any type of predictive analytics. Hence, organizations are confronted with a dilemma in which they need to make a tradeoff between a sparse use of data and the utility from better predictive analytics. This paper proposes a masking mechanism that obscures sensitive attributes while maintaining a large degree of predictive power. More precisely, we efficiently identify data partitions that are best suited for (i) shuffling, (ii) swapping and, as a form of randomization, (iii) perturbing attributes by conditional replacement. By operating on data partitions that are derived from a predictive algorithm, we achieve the objective of masking privacy-sensitive attributes with marginal downsides for predictive modeling. The resulting trade-off between masking and predictive utility is empirically evaluated in the context of customer churn where, for instance, a stratified shuffling of attribute values impedes predictive accuracy rarely by more than a percentage point. Our proposed framework entails direct managerial implications as a growing share of firms adopts predictive analytics and thus requires mechanisms that better adhere to user demands for information privacy.