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abstract: 'In this paper we study solutions to elliptic linear equations $L(u)=\partial_i(a^{ij}(x)\partial_j u) + b^i(x) \partial _i u + c(x) u=0$, either on ${\mathds{R}}^n$ or a Riemannian manifold, under the assumption of Lipschitz control on the coefficients $a^{ij}$. We focus our attention on the critical set ${\mathcal{C}}(u)\equiv\{x:|\nabla u|=0\}$ and the singular set ${\mathcal{S}}(u)\equiv\{x:u=|\nabla u|=0\}$, and more importantly on effective versions of these. Currently, under the coefficient control we have assumed, the strongest results in the literature say that the singular set is $n-2$-dimensional, however at this point it has not even been shown that ${\mathcal{H}}^{n-2}({\mathcal{S}})<\infty$ unless the coefficients are smooth. Fundamentally, this is due to the need of an $\epsilon$-regularity theorem which requires higher coefficient control as the frequency increases. We introduce new techniques for estimating the critical and singular set, which avoids the need of any such $\epsilon$-regularity. Consequently, we prove that if the frequency of $u$ is bounded by $\Lambda$ then we have the estimates ${\mathcal{H}}^{n-2}({\mathcal{C}}(u))\leq C^{\Lambda^2}$, ${\mathcal{H}}^{n-2}({\mathcal{S}}(u))\leq C^{\Lambda^2}$, depending on whether the equation is critical or not. More importantly, we prove corresponding estimates for the [*effective*]{} critical and singular sets. Even under the assumption of analytic coefficients these results are much sharper than those currently in 