I will show how to construct gauge-invariant and U-duality covariant expressions for Wess-Zumino terms corresponding to general Dp-branes in arbitrary D less than 10 dimensions. A distinguishing feature of these Wess-Zumino terms is that they contain twice as many scalars as the 10-D compactified dimensions, in line with doubled geometry. It turns out that For D less than 10 the charges of the higher-dimensional branes can all be expressed as products of the 0-brane charges, which include the D0-brane and the NS-NS 0-brane charges. I will show how the general expressions for these charges determine the non-trivial conjugacy class to which some of the higher-dimensional D-branes belong. Some implications and extensions of our work will be discussed.