Reversible programming languages guarantee that their programs are invertible at the cost of restricting the permissible operations to those which are locally invertible. However, writing programs in a reversible style can be cumbersome, and may produce significantly different implementations than the conventional – even when the implemented algorithm is, in fact, invertible. We introduce Jeopardy, a functional programming language that guarantees global program invertibility without imposing local invertibility. In particular, Jeopardy allows the limited use of uninvertible – and even nondeterministic – operations, provided that they are used in a way that can be statically determined to be globally invertible. To this end, we outline an implicitly available arguments analysis and further approaches that can give a partial static guarantee to the (generally difficult) problem of guaranteeing invertibility.