Using analytic calculations and N-body simulations we show that in constant density (harmonic) cores, sinking satellites undergo an initial phase of very rapid (super-Chandrasekhar) dynamical friction, after which they experience no dynamical friction at all. For density profiles with a central power law profile, ρ ∝ r -α, the infalling satellite heats the background and causes α to decrease. For α < 0.5 initially, the satellite generates a small central constant density core and stalls as...