We characterize the bounded derivations from the disc algebra to its dual in
terms of a natural `symbol' function. This is the first non-trivial uniform
algebra for which such a characterisation has been obtained.

As an immediate corollary we show that all such derivations are automatically
compact, resolving a question raised by S. E. Morris. We also give the first
construction of explicit "Pietsch control measures" for such derivations, thus
obtaining an independent proof that they are 2-summing.