Rational families of instanton bundles on $\mathbb P^{2n+1}$

I'll discuss the rationality problem for two kinds of moduli spaces for instanton bundles on $\mathbb P^{2n+1}$, namely for special instantons in the sense of Spindler-Trautmann and for symplectic 't Hooft instantons in the sense of Ottaviani. The latter is joint work with Costa, Miro-Roig and Schmitt.