  We show that a suitable background field can bring a non-BPS topological
soliton into its BPS, self-dual, counterpart. As an example we consider
Skyrmions in the minimal Skyrme model. We prove the triviality of the
corresponding moduli space. This means that the resulting self-dual Skyrmion
does statically interact with the background field. We also show that the
originally self-dual Skyrmions (e.g. solutions of the BPS Skyrme model) can
preserve the self-duality after a coupling with a background field. In this
case, BPS Skyrmions can be effortless moved with respect to the background.
