With the randomization approach, sensitive data items of records are randomized to protect privacy of individuals while allowing the distribution information to be reconstructed for data analysis. In this paper, we distinguish between reconstruction that has potential privacy risk, called micro reconstruction, and reconstruction that does not, called aggregate reconstruction. We show that the former could disclose sensitive information about a target individual, whereas the latter is more useful for data analysis than for privacy breaches. To limit the privacy risk of micro reconstruction, we propose a privacy definition, called (epsilon,delta)-reconstruction-privacy. Intuitively, this privacy notion requires that micro reconstruction has a large error with a large probability. The promise of this approach is that micro reconstruction is more sensitive to the number of independent trials in the randomization process than aggregate reconstruction is; therefore, reducing the number of independent trials helps achieve (epsilon,delta)-reconstruction-privacy while preserving the accuracy of aggregate reconstruction. We present an algorithm based on this idea and evaluate the effectiveness of this approach using real life data sets.