  We present a new method for finding lower bounds on the energy of topological
cosmic string solutions in gravitational field theories. This new method
produces bounds that are valid over the entire space of solutions, unlike the
traditional approach, where the bounds obtained are only valid for
cylindrically symmetric solutions. This method is shown to be a generalisation
of the well-known Bogomol'nyi procedure for non-gravitational theories and as
such, it can be used to find gravitational Bogomol'nyi bounds for models
wherever the traditional Bogomol'nyi procedure can be applied in the
non-gravitational limit. Furthermore, this method yields Bogomol'nyi equations
that do not rule out the existence of asymmetric bound-saturating solutions.
