Charges and fields in a straight, infinite, cylindrical wire carrying a steady current are determined in the rest frames of ions and electrons, starting from the standard assumption that the net charge per unit length is zero in the lattice frame and taking into account a self-induced pinch effect. The analysis presented illustrates the mutual consistency of classical electromagnetism and special relativity. Some consequences of the assumption that the net charge per unit length is zero in the electron frame are also briefly discussed. (Contains 1 footnote.)