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The longstanding problem of moving discrete solitary waves in nonlinearSchr{\"o}dinger lattices is revisited. The context is photorefractive crystallattices with saturable nonlinearity whose grand-canonical energy barriervanishes for isolated coupling strength values. {\em Genuinely localisedtravelling waves} are computed as a function of the system parameters {\it forthe first time}. The relevant solutions exist only for finite velocities.Comment: 5 pages, 4 figure

Radiationless Traveling Waves in Saturable Nonlinear Schrödinger Lattices