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It is well established that third-order nonlinearity produces a strong deviation from Gaussian statistics in water of infinite depth, provided the wave field is long crested, narrow banded and sufficiently steep. A reduction of third-order effects is however expected when the wave energy is distributed on a wide range of directions. In water of arbitrary depth, on the other hand, third-order effects tend to be suppressed by finite depth effects if waves are long crested. Numerical simulations of the truncated potential Euler equations are here used to address the combined effect of directionality and finite depth on the statistical properties of surface gravity waves; only relative water depth <i>kh</i> greater than 0.8 are here considered. Results show that random directional wave fields in intermediate water depths, <i>kh</i>=<i>O</i>(1), weakly deviate from Gaussian statistics independently of the degree of directional spreading of the wave energy.