Simple linear regression in the functional errors-in-variables (EIV) model is revisited from a different perspective, where the problem is addressed by using the small-sigma model instead of large sample theory. A general analysis is developed to study the slope's estimator that minimizes a family of objective functions, of which the least-squares fit and the maximum likelihood estimator are minimizers of such special functions. General formulas for the higher-order terms of the bias, the variance, and the mean square error are derived. Accordingly, two efficient estimators are proposed after implementing the pre- and the post-bias elimination techniques. Numerical tests confirm the superiority of the proposed estimators over others.