In the literature measures of fine-tuning have been discussed as one of the tools to assess the feasibility of beyond the Standard Model theories. In this paper we focus on two specific measures and investigate what kind of fine-tuning they actually quantify. First we apply both measures to the two Higgs doublet model, for which one can analyze the numerical results in terms of available analytic expressions. After drawing various conclusions about the fine-tuning measures, we investigate a particular left-right symmetric model for which it has been claimed that already at tree-level it suffers from a high amount of fine-tuning. We will reach a different conclusion, although left-right symmetric models may require a modest amount of fine-tuning if phenomenological constraints are imposed. Our analysis shows that the two considered measures can probe different aspects of fine-tuning and are both useful if applied and interpreted in the appropriate way. (C) 2019 The Author(s). Published by Elsevier B.V.