  We extend Dixmier's construction of singular traces (see \cite{Dixmier}) to
arbitrary fully symmetric operator ideals. In fact, we show that the set of
Dixmier traces is weak$^*$ dense in the set of all fully symmetric traces (that
is, those traces which respect Hardy-Littlewood submajorization). Our results
complement and extend earlier work of Wodzicki \cite{Wodzicki}.
