This paper presents a Bayesian analysis of a single equation from a simultaneous equations system. The analysis is carried out under "limited information" because no prior information (other than a list of endogenous and exogenous variables) is introduced on the parameters of the remaining equations in the in the system. These parameters are integrated out analytically. The equation of interest may or may not be identified by means of exact a priori information; probabilistic prior information is equally acceptable. The prior density is either of the non-informative or the natural conjugate type. The kernel of the posterior density for the regression coefficients is a ratio of t kernels. The existence of posterior moments is ascertained. This approach is applied for illustrative purposes to Tintner's model of the meat market.