This paper presents a new interactive procedure, Local Slant-Sum Adaptive Noise Removal (LSSANR), for attenuating linear, coherent, noise modes in the time-space domain. The procedure uses either a fixed or a sliding window to estimate noise wavelets and then subtracts the noise wavelets from the seismic traces on shot records. The procedure can adapt to dispersive noise in local, time-space windows, thereby minimizing smearing associated with filtering. Because the algorithm can attenuate ground roll and refraction first-arrivals, it may be especially useful in geotechnical and environmental seismic reflection surveys in which low fold, weak reflections are commonly obscured by these other two events. Synthetic examples and a field data case show that the algorithm is also successful in attenuating multiple noise events.