All methods presented in textbooks for computing inverse "Z"-transforms of rational functions have some limitation: 1) the direct division method does not, in general, provide enough information to derive an analytical expression for the time-domain sequence "x"("k") whose "Z"-transform is "X"("z"); 2) computation using the inversion integral method becomes labored when "X"("z")[superscript zk-1] has poles at the origin of the complex plane; 3) the partial-fraction expansion method, in spite of being acknowledged as the simplest and easiest one to compute the inverse "Z"-transform and being widely used in textbooks, lacks a standard procedure like its inverse Laplace transform counterpart. This paper addresses all the difficulties of the existing methods for computing inverse "Z"-transforms of rational functions, presents an easy and straightforward way to overcome the limitation of the inversion integral method when "X"("z")[superscript zk-1] has poles at the origin, and derives five expressions for the pairs of time-domain sequences and corresponding "Z"-transforms that are actually needed in the computation of inverse "Z"-transform using partial-fraction expansion. (Contains 3 tables and 1 footnote.)