Portland cements of type and category CEM I 52.5 R are governed by standard UNE-EN 197-1. These cements additionally have a granulometric distribution with a Blaine fineness greater than 6500 cm2/g, a tricalcium silicate content, C3S, greater than 55% by weight and a tricalcium aluminate content, C3A, greater than 4% and less than 25% by weight and with a sum of both greater than 75%. These cements have a strength according to UNE 196-1 at 1 day greater than 40 MPa and at 28 days greater than 65 MPa. Mixtures of these cements with a common cement are governed by standard UNE-EN 197-1. These mixtures present high mechanical performance at short ages. A procedure obtains these mixtures and their use in the manufacture of cement derivatives, such as concretes, mortars and slurries.