A roll of composite wrap material for successively and individually wrapping outer perimeters of bales of agricultural material with a characteristic outer perimeter length, the roll of composite wrap material comprising: a length of net wrap configured as a plurality of segments of net wrap (70, 100, 130, 160), each of the plurality of segments of net wrap (70, 100, 130, 160) being configured with a length (72, 102, 132, 162) that is longer than the outer perimeter length of a bale to be wrapped and with a width (74, 104, 134, 164) that is at least as wide as a bale to be wrapped, the segments of net wrap (70, 100, 130, 160) being arranged end to end, with respect to the lengths (72, 102, 132, 162) of the segments of net wrap (70, 100, 130, 160), along the length of net wrap; a plurality of first barrier segments of semi-permeable material (76, 106, 136, 166) configured to be substantially permeable to water vapor, each first barrier segment of semi-permeable material (76, 106, 136, 166) being disposed to overlay with a corresponding one of the segments of net wrap (70, 100, 130, 160); characterized in further comprising a plurality of second barrier segments of material (86, 116, 146, 176), each of the second barrier segments of material (86, 116, 146, 176) being disposed to overlay, at least in part, with a corresponding one of the first barrier segments of semi-permeable material (76, 106, 136, 166) and with the segment of net wrap (70, 100, 130, 160) associated with the corresponding first barrier segment of semi-permeable material (76, 106, 136, 166); wherein, when the wrap material is wrapped around a bale, the overlay of the second barrier segments of material (86, 116, 146, 176) with the first barrier segments of semi-permeable material (76, 106, 136, 166) forms first and second barrier layers for the bale to impede movement of liquid water from outside the composite wrap material to the outer perimeters of the bale. a length of net wrap configured as a plurality of segments of net wrap (70, 100, 130, 160), each of the plurality of segments of net wrap (70, 100, 130, 160) being configured with a length (72, 102, 132, 162) that is longer than the outer perimeter length of a bale to be wrapped and with a width (74, 104, 134, 164) that is at least as wide as a bale to be wrapped, the segments of net wrap (70, 100, 130, 160) being arranged end to end, with respect to the lengths (72, 102, 132, 162) of the segments of net wrap (70, 100, 130, 160), along the length of net wrap; a plurality of first barrier segments of semi-permeable material (76, 106, 136, 166) configured to be substantially permeable to water vapor, each first barrier segment of semi-permeable material (76, 106, 136, 166) being disposed to overlay with a corresponding one of the segments of net wrap (70, 100, 130, 160); characterized in further comprising a plurality of second barrier segments of material (86, 116, 146, 176), each of the second barrier segments of material (86, 116, 146, 176) being disposed to overlay, at least in part, with a corresponding one of the first barrier segments of semi-permeable material (76, 106, 136, 166) and with the segment of net wrap (70, 100, 130, 160) associated with the corresponding first barrier segment of semi-permeable material (76, 106, 136, 166); wherein, when the wrap material is wrapped around a bale, the overlay of the second barrier segments of material (86, 116, 146, 176) with the first barrier segments of semi-permeable material (76, 106, 136, 166) forms first and second barrier layers for the bale to impede movement of liquid water from outside the composite wrap material to the outer perimeters of the bale.