This review brings some new insights on erythrocytosis of genetic origin related to problems of oxygen delivery by hemoglobin (Hb). A few molecular mechanisms are individualized among the about 100 Hb variants that cause compensatory erythrocytosis. The most frequently observed structural modifications are localized in the alpha1beta2 interface, or at the C-terminal. They impair formation of a stable T state. Others mutations modify directly or indirectly the surrounding of the heme and the site where oxygen binds. A special interest is brought to the dose effect considering the possibility for formation of hybrid tetramers with altered oxygen binding properties. Homozygous cases, and patients who are compound heterozygotes for a high oxygen affinity Hb and a thalassemia (thal), are discussed. Several examples are provided, specially documented for Hb Olympia [beta20(B2)Val --> Met] and Hb Saint Nazaire [beta103(G5)Phe --> Ile]. Other mechanisms leading to erythrocytosis are discussed, and finally, an algorithm is proposed for etiological diagnosis.