The effect of pressure-dependent slip at the wall in steady, isothermal, incompressible Poiseuille flows of a Newtonian liquid is investigated. Exponential dependence of the slip coefficient on the pressure is assumed and the flow problems are solved using a regular perturbation scheme in terms of the exponential decay parameter of the slip coefficient. The sequence of partial differential equations resulting from the perturbation procedure is solved analytically up to second order. The two-dimensional solution reveals the effects of the slip decay coefficient and the other dimensionless numbers and parameters, in the flow. The average pressure drop and the skin friction factor are also derived and discussed. (C) 2013 The Society of Rheology. [http://dx.doi.org/10.1122/1.4769823]