  We derive the leading exponential finite volume corrections in two
dimensional integrable models for non-diagonal form factors in diagonally
scattering theories. These formulas are expressed in terms of the infinite
volume form factors and scattering matrices. If the particles are bound states
then the leading exponential finite-size corrections ($\mu$-terms) are related
to virtual processes in which the particles disintegrate into their
constituents. For non-bound state particles the leading exponential finite-size
corrections (F-terms) come from virtual particles traveling around the finite
world. In these F-terms a specifically regulated infinite volume form factor is
integrated for the momenta of the virtual particles. The F-term is also present
for bound states and the $\mu$-term can be obtained by taking an appropriate
residue of the F-term integral. We check our results numerically in the
Lee-Yang and sinh-Gordon models based on newly developed Hamiltonian
truncations.
