The wrench-feasible workspace of cable-driven parallel robots can be represented as the solution of an underdetermined linear equation system bounded by lower and upper constraints. This paper proposes a new method to project the resulting double-inequality system onto a subspace in order to eliminate free variables that appear in the original solution. The resulting method is based on the well-known Fourier-Motzkin elimination (FME) algorithm and allows the computation of all minimal double-inequalities bounding the projected solution region. It takes advantage of the specific structure of double-inequality systems to reduce the number of redundant inequalities resulting from the initial algorithm. A notation for double-inequality systems is also proposed to simplify the expression of the FME when applied to such problems. Finally, an example applying the resulting modified FME (mFME) method to the computation of the wrench-feasible workspace for a simple planar cable robot is presented.