I know that every generalised (Eilenberg-Steenrod) cohomology theory defines a spectrum (in the sense of Lewis-May), and vice-versa. I also know that maps between spectra are richer than maps between cohomology theories (due to the existence of phantom maps).
How unique is the/a spectrum representing a cohomology theory?
In particular, are Eilenberg-MacLane spectra unique up to weak equivalences? (An Eilenberg-MacLane spectrum for the abelian group $A$ is a spectrum representing ordinary cohomology with coefficients in $A$.)