Summary: The balanced Procrustes problem with some special constraints such as symmetric orthogonality and symmetric idempotence are considered. By one time eigenvalue decomposition of the matrix product generated by the matrices $A$ and $B$, the constrained solutions are constructed simply. Similar strategy is applied to the problem with the corresponding $P$-commuting constraints with a given symmetric matrix $P$. Numerical examples are presented to show the efficiency of the proposed methods.