ABSTRACT A compact object moving relative to surrounding gas accretes material and perturbs the density of gas in its vicinity. In the classical picture of Bondi–Hoyle–Lyttleton accretion, the perturbation takes the form of an overdense wake behind the object, which exerts a dynamical friction drag. We use hydrodynamic simulations to investigate how the accretion rate and strength of dynamical friction are modified by the presence of outflow from the compact object. We show that the destruction of the wake by an outflow reduces dynamical friction, and reverses its sign when the outflow is strong enough, in good quantitative agreement with analytic calculations. For a strong isotropic outflow, the outcome on scales that we have simulated is a negative dynamical friction, i.e. net acceleration. For jet-like outflows driven by reprocessed accretion, both the rate of accretion and the magnitude of dynamical friction drop for more powerful jets. The accretion rate is strongly intermittent when the jet points to the same direction as the motion of the compact object. The dynamical effects of outflows may be important for the evolution of compact objects during the common envelope phase of binary systems, and for accreting compact objects and massive stars encountering active galactic nucleus discs.