The standard quasi-experimental approach in applied econometric research requires the adoption of so-called orthogonality conditions. An initial set of such conditions has to be justified on the basis of persuasive economic theoretical arguments – which by contenders may be qualified as opportunistic subjective beliefs – since these conditions cannot be vindicated by empirical statistical inference. Formal testing of any overidentification restrictions is only feasible conditional on the validity of this initial identifying set. For the analysis of single equations this implies that at least as many included explanatory and excluded instrumental variables have to be proclaimed being (weakly-)exogenous for the parameters of interest as there are unknown coefficients to be estimated. It can be shown, however, that there are alternative routes towards identification by adopting probably more credible non-orthogonal moment conditions. We demonstrate how least-squares confidence intervals – which are improper under simultaneity – can be transformed into informative intervals when exploiting arbitrary bounds on the degree of non-orthogonality or simultaneity. We discuss the consequences for some widely-cited empirical studies on macro and micro economic relationships, such as: Effect of police on crime (Levitt, AER 1997), Effect of aid on growth (Rajan and Subramanian, RES 2008), Does trade cause growth (Frankel and Romer, AER 1999), Effects of childbearing on labor supply (Angrist and Evans, AER 1998), Wage returns to schooling (Angrist and Krueger, QJE 1991).