This study shows the effect of changing the way ice histories are implemented in Glacial Isostatic Adjustment (GIA) codes to solve the sea level equation. The ice history models are being constantly improved and are provided in different formats. The overall algorithmic design of the sea-level equation solver often forces to implement the ice model in a representation that differs from the one originally provided. We show that using different representations of the same ice model gives important differences and artificial contributions to the sea level estimates, both at global and at regional scale. This study is not a speculative exercise. The ICE-5G model adopted in this work is widely used in present day sea-level analysis, but discrepancies between the results obtained by different groups for the same ice models still exist, and it was the effort to set a common reference for the sea-level community that inspired this work. Understanding this issue is important to be able to reduce the artefacts introduced by a non-suitable ice model representation. This is especially important when developing new GIA models, since neglecting this problem can easily lead to wrong alignment of the ice and sea-level histories, particularly close to the deglaciation areas, like Antarctica.