Methods are presented for treating cancers and hematopoietic stem cell disorders, comprising administering to a subject with a cancer or hematopoietic stem cell disorder who is receiving a treatment regimen, a heparin derivative capable of inhibiting, reducing, abrogating or otherwise interfering with the binding of CXCL12 to CXCR4, wherein the cancer or hematopoietic stem cell disorder is one in which interaction of CXCL12 with CXCR4 privileges the cancer or disordered HSCs against therapeutic intervention. In preferred embodiments, the heparin derivative is a substantially 2-O, 3-O-desulfated heparin derivative.