A process for production of very high-quality base oils, and simultaneous production of high-quality middle distillates, comprises the successive stages of hydroisomerization and catalytic dewaxing. The hydroisomerization takes place in the presence of a catalyst containing at least one noble metal deposited on an amorphous acid support, the metal dispersion being less than 20%. The support is preferably an amorphous silica-alumina. The catalytic dewaxing takes place in the presence of a catalyst containing at least one hydrodehydrogenating element (Group VIII) and at least one molecular sieve chosen from ZBM-30, EU-2, and EU-11.