A tilling cultivator and associated method is disclosed for strip tilling cover crop in preparation for primary crop planting. The tiller includes a pressing drum having a band coulter for cutting surface and subsurface cover crop residue roots and compressing the cover crop into the soil. A trailing shank just behind and aligned with the coulter clears debris from the planting furrow, and a pair of staggered wavy coulters behind the shank closes any shank voids. A rolling basket or other optional soil conditioners trail behind the planting furrow to create a suitable seedbed for primary crop planting. The apparatus and an associated method of use aids in cover crop decomposition and pre-plant field preparation.