Very strong difference in many properties is well documented for graphite oxides (GtO) synthesized by Brodie (BGO) and Hummers (HGO) methods. The difference is typically assigned to the type of oxidant (chlorates or KMnO4, respectively). However, not only oxidants but also acids used in these methods are different. It is still unclear which of the different properties of GtO are dependent on the oxidant or acid used in the synthesis. Here we synthesized a new type of graphite oxide using an oxidation agent typical for the Brodie method (KClO3) in combination with acids so far used only in modified Hummers' method (H2SO4+H3PO4). The GtO synthesized by this method (MGO) demonstrates some properties similar to BGO (higher temperature of exfoliation and less defected structure) but also similarity to some other properties of HGO (absence of sharp swelling transitions). Comparing MGO, BGO, and HGO allows us to distinguish the effects of acids and oxidants on the properties of graphite oxides. The new procedure proposed in this study allows preparation of GtO nearly free from hole/vacancy defects (similarly to BGO) but avoids dangerous HNO3. MGO is suggested as a favorable precursor for the preparation of graphene films by thermal or chemical reduction methods.