We study coherent wave scattering through waveguides with a step-like surface disorder and find distinct enhancements in the reflection coefficients at well-defined resonance values. Based on detailed numerical and analytical calculations, we can una
mbiguously identify the origin of these reflection resonances to be higher-order correlations in the surface disorder profile which are typically neglected in similar studies of the same system. A remarkable feature of this new effect is that it relies on the longitudinal correlations in the step profile, although individual step heights are random and thus completely uncorrelated. The corresponding resonances are very pronounced and robust with respect to ensemble averaging, and lead to an enhancement of wave reflection by more than one order of magnitude.
