We show that optimizing a quantum gate for an open quantum system requires the time 
evolution of only three states irrespective of the dimension of Hilbert space. This 
represents a significant reduction in computational resources compared to the complete
basis of Liouville space that is commonly believed necessary for this task. The 
reduction is based on two observations: The target is not a general dynamical map but 
a unitary operation; and the time evolution of two properly chosen states is 
sufficient to distinguish any two unitaries. We illustrate gate optimization employing
a reduced set of states for a controlled phasegate with trapped atoms as qubit 
carriers and a viSWAP gate with superconducting qubits.