Keeping the volume of connections in the cortex as low as possible may be an important evolutionary constraint on the design of the brain. Much as an engineer tries to arrange the components of a computer in such a way as to give efficient wiring, so the brain may have evolved a layout of neuronal types which gives an economical use of axonal 'wiring'. One key difference between computer and brain is that connections in the brain take the form of elaborate branching structures. It is argued here that certain features of cortical mapping, such as the stripes and patches seen within cortical areas, may be adaptations which allow efficient wiring by such structures. Some simple calculations are given to support this, using as models for axonal arbors certain branching patterns which give a low volume of wiring. In particular, it is shown that a pattern of stripes can give economical wiring when axon diameters follow a law dp = dp1 + dp2 with p greater than 4, where d1 and d2 are the diameters of the daughter branches and d that of the parent.