From the point where the range of Brownian motion attains a target value we define, looking both backward and forward, a decomposition of the path into pieces for which the extremities give the two extremal ordinates. Explicit joint laws for the duration and width of the pieces have a simple form. Moved to start at the origin and taken in absolute value, the pieces are shown to be, conditionally on their widths, independent BES3(0) processes run until they first hit the respective widths.