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A differential pulse-width pair (DPP) Brillouin distributed fiber sensor is implemented to achieve centimetric spatial resolution over distances of several kilometers. The presented scheme uses a scanning method in which the spectral separation between the two probe sidebands is kept constant, while the optical frequency of the pump is swept to scan the Brillouin spectral response. Experimental results show that this method avoids detrimental temporal distortions of the pump pulses, which in a standard implementation prevent the DPP method from operating over mid-to-long distances. Such a novel scanning procedure allows the resolving, for the first time in pure time-domain Brillouin sensors, of 1,000,000 sensing points, i.e., 1 cm spatial resolution over 10 km in a conventional acquisition time.