To tackle the problem of climate change, Swiss energy strategies aim to reach the carbon neutrality by 2050. However, this challenge cannot simply be solved by focusing on the operational energy performance and instead, on a lifecycle evaluation. Thus, in order to reduce the sector's carbon footprint, building stakeholders need to consider embodied GHG emissions of construction materials. In this study, a parametric method was developed to balance operational and embodied impacts of insulation strategies on GHG emissions according to the material and heating system choices. The methodology is split into two for the computation of the overall carbon emissions of the heating plus insulation system. Firstly, the calculation of the embodied emissions, which relies on Environmental Product Declarations of different construction materials. Secondly, the calculation of the operational emissions, which is the product between the thermal energy needs and the energy carbon content of the respective heating system. Thereafter, the methodology was applied to two case studies: an existing building and a brand-new building. The first main finding was that, for high-carbon insulation materials, there was clearly an optimal thickness after which, adding insulation would only increase the lifecycle impact of the system. For instance, in the heat-pump equipped case study, installing 35 cm of extruded polystyrene insulation (XPS) is more harmful towards global warming than installing 17 cm of XPS. This trend was not present for low-carbon materials whatsoever. The building's carbon emissions benefitted from their addition of insulation up to the maximum thicknesses studied. To conclude, it is also important to highlight that aimlessly targeting energy efficiency can be a step back towards the goal of carbon neutrality. Indeed, it is possible to claim that for energy efficient buildings, fossil fuel-based insulation should be carefully used. This study allowed the development and application of a method that identifies optimal insulation thickness and material for a given heating system and hopefully, highlight the importance of considering both embodied and operational emissions of construction materials and systems.