We consider PDE-constrained optimization problems that are governed by an elliptic or a parabolic differential equation of second order. We are interested in problems with limited observation. The solution to this problem is characterized by the first order optimality system, which is a linear system of variational equations for state y and adjoined state p that has saddle point structure. For the parabolic problem, it the variational equations involve the whole space-time cylinder. We are interested in a preconditioner where the condition number of the preconditioned system is robust in the relevant model parameters (like diffusion coefficient or regularization parameter in tracking functional) and discretization parameters (like grid size and spline degree). If we restrict ourselves to the case of full observation, there is a symmetry between the state and the adjoined state, which lead to the construction of several families of robust preconditioners, like those by Schöberl and Zulehner and those by Pearson and Wathen. We proposer a preconditioner that does not require this symmetry. It is based on a Schur complement formulation for the state, which leads to a formulation that requires H^2-regularity in space and (for the parabolic problem) H^1-regularity in time. In order to obtain a conforming discretization, we need C^1 smooth basis functions. While this would need quite some effort with standard finite element methods, in Isogeometric Analysis such basis functions can be set up with ease. We will see that the condition number estimates follow trivially if the space used for the discretization of the adjoined state contains Ly_h, i.e., the result of applying the differential operator L to the discretized state y_h. In general, this leads to a rather large number of degrees of freedom for the adjoined state, compared to the state. We will see that condition number estimates also hold if the adjoined state does not contain Ly_h, which allows for the reduction of the spline spaces.