Two ideals \(I, J\) of a Noetherian ring \(R\) are said to be projectively equivalent when the integral closures \((I^i)_a\), \((J^j)_a\) are equal for some \(i, j\) of \(\mathbb{N}\). This note continues the work of the second author in investigating the interplay between projective equivalence and the properties of the form rings \(F(R,I)=\oplus^\infty_{n=0} I^n/I^{n+1}\). The results which are of a technical nature are mostly of the form: for all ideals \(I\) of a certain type of Noetherian ring \(R\) there exists a projectively equivalent ideal \(J\) such that the set of associated prime ideals of zero in \(F(R,J)\) is restricted in some way. It is shown for example that the completion of a semilocal ring \(R\) has no embedded prime divisors of zero if, and only if, for all ideals \(I\) of \(R\) there exists a projectively equivalent ideal \(J\) such that \(F(R,J)\) has no embedded prime divisors of zero. Similarly amongst other characterizations of locally unmixed Noetherian rings it is shown that \(R\) is locally unmixed if, and only if, for all ideals \(I\) of \(R\) there exists a projectively equivalent ideal \(J\) such that \(F(R,J)\) has no embedded prime divisors of zero and at each maximal ideal the localization of \(F(R,J)\) satisfies the second chain condition.