We focus on two mainstream privacy models: k-anonymity and differential privacy. Once a privacy model has been selected, the goal is to enforce it while preserving as much data utility as possible. The main objective of this thesis is to improve the data utility in k-anonymous and differentially private data releases. k-Anonymity has several drawbacks. On the disclosure limitation side, there is a lack of protection against attribute disclosure and against informed intruders. On the data utility side, dealing with a large number of quasi-identifier attributes is problematic. We propose a relaxation of k-anonymity that deals with these issues. Differential privacy limits disclosure risk through noise addition. The Laplace distribution is commonly used for the random noise. We show that the Laplace distribution is not optimal: the same disclosure limitation guarantee can be attained by adding less noise. Optimal univariate and multivariate noises are characterized and constructed. Common mechanisms to attain differential privacy do not take into account the users prior knowledge; they implicitly assume zero initial knowledge about the query response. We propose a mechanism that focuses on limiting the knowledge gain over the prior knowledge. Microaggregation-based k-anonymity and differential privacy can be combined to produce microdata releases with the strong privacy guarantees of differential privacy and improved data accuracy. The last contribution delves into the relation between t-closeness and differential privacy. We see that for a specific distance and under some reasonable assumptions on the intruders knowledge, t-closeness leads to differential privacy.