'Sustainable intensification' of agriculture implies improving efficiency, increasing inputs and/or outputs per land area and minimizing environmental impacts. Dairy farm intensification can be achieved at both animal and farm levels but whether or not it is environmentally 'sustainable' is an ongoing debate. Both practices fail to account for environmental impacts associated with the production of external inputs, which also relates to a farm's self-sufficiency level, i.e. its capacity to produce goods from its own resources, with higher control over nutrient recycling and thus minimization of losses to the environment. This study explored the relationship of a 'global' (on and off-farm impacts) eco-efficiency indicator with on-farm practices promoting (animal and farm-level) intensification and self-sufficiency of French specialized dairy farms. The relationships were expressed using Partial Least Squares Structural Equation Modelling to build, and relate, latent variables of eco-efficiency, intensification and self-sufficiency. The latent variables for intensification and self-sufficiency were determined by proxy indicators obtained from a Life Cycle Assessment (LCA) exercise. The latent variable for eco-efficiency was represented by an aggregate eco-efficiency score per farm derived from a Data Envelopment Analysis model by again using LCA data. The dataset was split into two spatially heterogeneous (bio-physical conditions, production patterns) regions. For both regions, results identified a significant negative relationship between eco-efficiency and practices increasing milk yield/cow and the use of maize silage and imported concentrates. However, these results might not necessarily hold for intensive farms with better ability to recycle elements on-farm. This requires further investigation with latent variables for intensification and self-sufficiency that do not largely overlap- a modelling challenge that occurred here. It stresses though the importance of self-sufficiency as an agro-ecological concept towards the design of intensive yet sustainable dairy farming systems. In conclusion, the debate whether or not intensive dairy farming is 'sustainable' remains open, however increasing self-sufficiency could offer a way to improve eco-efficiency.