Cross-efficiency analysis in DEA generally uses a two-stage procedure: first, optimize a DMU’s individual efficiency score; next, push the efficiencies of all DMUs in a desired direction. In order to reduce subjective judgement in the second step, we provide a cross-efficiency method using only strong defining hyperplanes of the underlying technology. We develop a new DEA-based algorithm, and prove its finiteness and correctness. To reduce the computational burden, we show how one can combine the procedure with a known beneath-and-beyond procedure. Numerical investigations—comprising real-world data—demonstrate the superiority of the new method.