A method of compacting a mat of hot mix asphalt which has been laid by an advancing asphalt paver, the method comprising advancing an asphalt compactor over the laid asphalt such that a compaction surface of the compactor, formed by a lower run of at least one belt, is engaged with any one portion of the mat for a period of at least 1.5 seconds, the compaction surface applying a maximum average load stress to the mat of less than about 50 kPa (7.252 psi). Compaction may be achieved using a compactor (60) comprising two longitudinally spaced modular compaction units (62) connected relative to each other, and a power source for driving at least one of the modular compaction units (62), wherein at least one of the modular compaction units (62) is adjustable to permit steering of the compactor, and wherein each of said modular compaction units (62) comprises a compaction belt (74), support means (78, 80) for the belt to define a planar lower run of the belt (74) forming a compaction surface.