Motion of wave energy converters (WECs) is usually exaggerated as a consequence of the application of control strategies for energy absorption maximisation. With the aim of preserving the physical integrity of the devices, constraint handling mechanisms, as part of the underlying control strategies, are considered a key component. Recent developments in wave energy control include a linear time-invariant-based controller presented in the literature as LiTe-Con, which provides a simple constraint handling mechanism. However, this handling method can lead to conservative performance in certain scenarios. To overcome such limitations, this study presents a time-varying methodology for an online adaptation of the constraint handling mechanism in LiTe-Con, while preserving its original simplicity and efficiency. Experimental assessment of the presented control methodology is provided in this study, using a broad range of operating conditions. Results show that the presented control strategy (LiTe-Con+) exceeds the performance achievable with the original LiTe-Con. Additionally, the benefits of LiTe-Con+, such as low computational demand, technical versatility, and impressive performance level are highlighted.