  Using thermodynamic arguments treatment it is shown that, independently on
whether Fisher renormalization changes the critical exponents near a phase
transition in a constrained system or not, new corrections to scaling with
correction exponents proportional to the specific heat index $\alpha$ appear.
Because of the smallness $\alpha$ for the Ising, the XY, and the Heisenberg
universality classes these corrections are dominant and can cause strong
crossover effects. It is proven that the appearance of Fisher corrections to
scaling is a quite general feature of the systems with constraints.
