When a Brownian object is in a non-equilibrium steady state, the actual force exerted on it is different from the one in thermal equilibrium. In our previous paper (Fruleux et al 2012 Phys. Rev. Lett. 108 160601), we discovered a general principle that relates the missing force to dissipation rates through the concept of momentum deficiency due to dissipation (MDD). In this paper, we examine the principle using various models based on hard disc gases and Brownian pistons. Explicit expressions of the forces are obtained analytically and the results are compared with molecular dynamics simulations. The good agreement demonstrates the validity of MDD. © 2012 The Royal Swedish Academy of Sciences.