We scrutinize the possibility of extending the result of  to the case of q-deformed oscillator for q real; for this we exploit the whole range of the deformation parameter as much as possible. We split the case into two depending on whether a solution of the commutation relation is bounded or not. Our leitmotif is subnormality. The deformation parameter q is reshaped and this is what makes our approach effective. The newly arrived parameter, the operator C, has two remarkable properties: it separates in the commutation relation the annihilation and creation operators from the deformation as well as it q-commutes with those two. This is why introducing the operator C may have far-reaching consequences.