A Lagrange multipliers method is shown to be a convenient way of applying constraints to a Newton-Raphson minimization algorithm in a conformational analysis program. To illustrate this method two applications are dealt with in some detail. The Eckart conditions are used as a set of constraints to avoid mathematical difficulties associated with the empirical valence-force potential in a conformational analysis problem. For the molecules considered the use of constraints speeds up the Convergence. The second application illustrates how the method can be used to study selected sections through potential energy surfaces.