Nonlinear inverse problems arising in dynamic system state/parameter estimation are generally non-convex, and possess multiple local minima that may threaten the convergence of global optimization routines. This problem is generally addressed by multiple starting point based algorithms. An alternative approach is to use the recently proposed concept of safe redundancy in order to derive an algorithm that crosses singularities by exploiting the particular nature of dynamic inverse problems. These techniques might seem similar, at least at first. The present communication aims to provide insight into the difference between these two approaches. This is accomplished through a simple illustrative example.