Mineral magnetic measurements are used to distinguish ice-rafted debris (IRD) sources and climate cycles spanning Marine Isotope Stage (MIS) 3 and MIS2 in core MD95-2006, from the Barra Fan, NE Atlantic. Distinct magnetic properties are displayed by IRD from the Laurentide ice sheet (LIS) (high susceptibility (chi), low isothermal remanent magnetization (IRM), low coercivity and the Verwey transition), the British ice sheet (BIS) (high chi, high IRM, medium coercivity and suppressed Verwey transition) and the ambient background sediment (low chi and low IRM). A magnetic unmixing model quantifies proportions of the IRD sources during Greenland Stadial (GS) 16 to GS3 (57.3 to 22.6 ka B. P.) spanning Heinrich Event (H) 5 to H2. The magnetic model suggests LIS IRD is only dominant within an interval during GS9, assigned to H4. Prior to H4 low proportions of BIS IRD suggest the BIS was not able to deliver significant amounts of IRD into the marine system. Following H4, proportions of BIS IRD during stadials increase, suggesting growth of the BIS during the latter stages of MIS3, with further expansion of the BIS during MIS2. LIS IRD within H2 is masked by BIS IRD input. Climatically driven anhysteretic remanent magnetizations reflect the short Dansgaard-Oeschger cycles between H5 and H4, while the proportions of hard magnetic minerals reflect the longer-term Bond cycles.