A two-pulse two-wave (Nd and CO₂ lasers) scheme is proposed for irradiating a laser target, which ensures the highest factor of laser radiation conversion to the X-ray range (13.5 nm ± 1%). Analytic estimates are obtained for parameters of pulses and of the target made of Xe or Li. Numerical optimization is performed for X-ray emission from a spherical Xe target exposed to a CO₂ laser pulse. The maximal factor of conversion of laser radiation to X rays is ∼1%. Angular and spectral characteristics of X-ray radiation are obtained. The flux of fast Xe ions ejected from the target and damaging the Mo/Si coating of X-ray mirrors is estimated.