The present paper attempts to demonstrate the great importance of innovative interventions οn the structural system of earthquake-resistant bridges. Τhe type of structural system affects also the construction method which will be chosen. The problem of selecting the most appropriate among the five current bridge construction methods (Cast-in-place, Precast I-Girder, Incremental Launching, Balanced Cantilever, Advanced Shoring method) is the most creative part of the decision-making process related to the construction of a bridge project. Seven compliance criteria are taken into account in this study, namely safety, economy, durability, serviceability, construction speed, aesthetics and environmental harmonization. The large number of criteria leads to the use of Multicriteria Analysis, and specifically of two Multicriteria methods: AHP and PROMETHEE. Certain innovative interventions in bridge design are selected and presented, all of them having features of "Egg of Columbus" solutions. Afterwards they are compared with some conventional construction methods, using a double Case study, from which interesting conclusions are drawn. The study does not result simply in the subjective predominance of one method, but in the hierarchy of all the respective alternative construction methods, followed by a specific score for each one of them. To this end, the opinions of distinguished experts on bridges are utilized through suitable questionnaires.