Summary: Let \(M^7\) be a smooth manifold equipped with a \(G_2\)-structure \(\phi\), and \(Y^3\) be a closed compact \(\phi\)-associative submanifold. R. C. McLean [Commun. Anal. Geom. 6, No. 4, 705–747 (1998; Zbl 0929.53027)] proved that the moduli space \(\mathcal{M}_{Y,\phi}\) of the \(\phi\)-associative deformations of \(Y\) has vanishing virtual dimension. In this paper, we perturb \(\phi\) into a \(G_2\)-structure \(\psi\) in order to ensure the smoothness of \(\mathcal{M}_{Y,\psi}\) near \(Y\). If \(Y\) is allowed to have a boundary moving in a fixed coassociative submanifold \(X\), it was proved in [the author and F. Witt, Adv. Math. 226, No. 3, 2351–2370 (2011; Zbl 1209.53040)] that the moduli space \(\mathcal{M}_{Y,X}\) of the associative deformations of \(Y\) with boundary in \(X\) has finite virtual dimension. We show here that a generic perturbation of the boundary condition \(X\) into \(X'\) gives the smoothness of \(\mathcal{M}_{Y,X'}\). In another direction, we use Bochner’s technique to prove a vanishing theorem that forces \(\mathcal{M}_{Y}\) or \(\mathcal{M}_{Y,X}\) to be smooth near \(Y\). For every case, some explicit families of examples will be given.