In a method for additive manufacturing, a multi-strand core reinforced filament including a flowable matrix material and substantially continuous reinforcing strands extending in a direction parallel to a length of the filament is supplied. A first consolidated composite swath of a height less than ½ the width of the filament is deposited in a first reinforcement formation including at least one straight path and at least one curved path against a deposition surface, and a second consolidated composite swath of a height less than ½ the width of the filament is deposited in a second reinforcement formation against the first consolidated composite swath. Each deposition flows the matrix material and applies an ironing force to spread the reinforcing strands within the filament against the underlying surface and/or previously deposited swath.