Unbalanced split-plot designs are considered, where the whole-plot treatments could be replicated an unequal number of times in the design, but each split-plot treatment occurs exactly once in every whole plot. Analysis of such designs is provided when the various effects could be fixed or random. In each case, valid exact tests and optimum invariant tests (whenever they exist) are derived for testing the significance of the various effects. In some cases optimum tests exist only under additional conditions on the design, and these conditions are specified for the various setups.