Privacy protection of confidential data is a fundamental problem faced by many government organizations and research centers. It is further complicated when data have complex structures or variables with highly skewed distributions. The statistical community addresses general privacy concerns by introducing different techniques that aim to decrease disclosure risk in released data while retaining their statistical properties. However, methods for complex data structures have received insufficient attention. We propose producing synthetic data via quantile regression to address privacy protection of heavy-tailed and heteroskedastic data. We address some shortcomings of the previously proposed use of quantile regression as a synthesis method and extend the work into cases where data have heavy tails or heteroskedastic errors. Using a simulation study and two applications, we show that there are settings where quantile regression performs as well as or better than other commonly used synthesis methods on the basis of maintaining good data utility while simultaneously decreasing disclosure risk.