Four mechanisms caused tephra fallout at Soufrière Hills Volcano, Montserrat, during the 1995-1999 period: explosive activity (mainly of Vulcanian type), dome collapses, ash-venting and phreatic explosions. The first two mechanisms contributed most of the tephra-fallout deposits (minimum total dense-rock equivalent volume of 23 x 10 m), which vary from massive to layered and represent the amalgamation of the deposits from a large numbers of events. The volume of co-pyroclastic-flow fallout tephra is in the range 4-16° of the associated pyroclastic flow deposits. Dome-collapse fallout tephra is characterized by ash particles generated by fragmentation in the pyroclastic flows and by elutriation of fines. Vulcanian fallout tephra is coarser grained, as it is formed by magma fragmentation in the conduit and by elutriation from the fountain-collapse flows and initial surges. Vulcanian fallout tephra is typically polymodal, whereas dome-collapse fallout tephra is predominantly unimodal. Polymodality is attributed to: overlapping of fallout tephra of different types, premature fallout of fine particles, multiple tephra-fallout sources, and differences in density and grain-size distribution of different components. During both dome collapses and explosions, ash fell as aggregates of various sizes and types. Accretionary lapilli grain size is independent of their diameter and is characterized by multiple subpopulations with a main mode at 5ø. Satellite data indicate that very fine ash can stay in a volcanic cloud for several hours and show that exponential thinning rates observed in proximal areas cannot apply in distal areas.