Summary: Let \(f:(\mathbb{C}^n,S)\rightarrow (\mathbb{C}^{n+1},0)\) be a germ whose image is given by \(g=0\). We define an \(\mathcal{O}_{n+1}\)-module \(M\)(\(g\)) with the property that \(\mathcal{A}_e\)-\(\operatorname{codim}(f)\le \operatorname{dim}_\mathbb{C}M(g)\), with equality if \(f\) is weighted homogeneous. We also define a relative version \(M_y(G)\) for unfoldings \(F\), in such a way that \(M_y(G)\) specialises to \(M\)(\(g\)) when \(G\) specialises to \(g\). The main result is that if \((n,n+1)\) are nice dimensions, then \(\operatorname{dim}_\mathbb{C}M(g)\ge \mu_I(f)\), with equality if and only if \(M_y(G)\) is Cohen-Macaulay, for some stable unfolding \(F\). Here, \(\mu_I(f)\) denotes the image Milnor number of \(f\), so that if \(M_y(G)\) is Cohen-Macaulay, then Mond’s conjecture holds for \(f\); furthermore, if \(f\) is weighted homogeneous, Mond’s conjecture for \(f\) is equivalent to the fact that \(M_y(G)\) is Cohen-Macaulay. Finally, we observe that to prove Mond’s conjecture, it is enough to prove it in a suitable family of examples.