Aims:We aim to understand the real nature of the stellar overdensity at southern galactic latitudes in the region of CMa. Methods: We perform a critical re-analysis and discussion of recent results presented in the literature which interpret the CMa overdensity as the signature of an accreting dwarf galaxy or a new substructure within the Galaxy. Several issues are addressed. Results: We show that arguments against the “warp” interpretation are based on an erroneous perception of the Milky Way. There is nothing anomalous with colour-magnitude diagrams on opposite sides of the average warp mid-plane being different. We witnessed the rise and fall of the blue plume population, first attributed to young stars in a disrupting dwarf galaxy and now discarded as a normal disc population. Similarly, there is nothing anomalous in the outer thin+thick disc metallicities being low (-1 < [Fe/H] < -0.5), and spiral arms (as part of the thin disc) should, and do, warp. Most importantly, we show unambiguously that, contrary to previous claims, the warp produces a stellar overdensity that is distance-compatible with that observed in CMa. Conclusions: The CMa over-density remains fully accounted for in a first order approach by Galactic models without new substructures. Given the intrinsic uncertainties (concerning the properties of the warp, flare and disc cutoff, the role of extinction and degeneracy), minor deviations with respect to these models are not enough to support the hypothesis of an accreted dwarf galaxy or new substructure within the Milky Way disc.