A new reservoir drilling fluid system utilizes a nonbiopolymer, acid- or enzyme-soluble polymer that serves both as viscosifier and fluid-loss additive when combined with activated magnesium oxide and a divalent-cation-based brine. The new fluid shows a unique shear-thinning rheological profile featuring relatively low, high-shear-rate viscosity along with relatively high, low-shear-rate viscosity. This behavior is highly unusual in high-density, brine-based reservoir drilling fluids. A result of this behavior is that effective hole cleaning is provided without generating excessive high-shear-rate viscosities that lead to disproportionate equivalent circulating densities. The new fluid system is based on the higher density, divalent-cation-containing brines (utilizing CaCl2, CaBr2, CaCl2 / CaBr2, ZnBr2 / CaBr2 and ZnBr2 /CaBr2 / CaCl2) in the 11.5 to 17.5 lb/gal density range. The total amount of the sized CaCO3 bridging particles is kept relatively low, 13 to 35 lb/bbl, so that thin, chemically removable filter cakes are produced. The size distribution of these bridging particles is designed according to the ideal packing sequence for optimizing sealing and producing a minimally invading (well productivity enhancing) fluid.