A general method is presented for determining an equilibrium point on a potential energy surface subject to an arbitrary number of constraints. The method is then specialized to the calculation of a conditional saddle point in the liquid-drop model for which the constraint is the mass-asymmetry degree of freedom. This approach is useful for cases in which the mass asymmetry is not one of the chosen coordinates but instead is a function of these coordinates. Conditional saddle points are calculated for the liquid-drop and Yukawa-plus-exponential nuclear energy models, with the nuclear shape parametrized using both a three-quadratic-surface model and a Legendre polynomial expansion of the nuclear surface function. We show how the conditional saddle-point shapes and energies change as the fissility x and the mass asymmetry value ..cap alpha.. are varied. As ..cap alpha.. increases for fixed x, the saddle-point configurations effectively behave like lighter (less fissile) nuclei. For fissilities less than the Businaro-Gallone value (x/sub BG/), the conditional saddle-point energy always decreases with increasing ..cap alpha... For x>x/sub BG/, with increasing ..cap alpha.. the conditional saddle-point energy increases until it reaches the limit of the Businaro-Gallone peak, after which the energy decreases.