We reconsider the problem of deforming a conformal field theory to a neighboring theory which is again critical. An invariant formulation of this problem is important for understanding the underlying symmetry of string theory. We give a simple derivation of A. Sen's recent formula for the change in the stress tensor and show that, when correctly interpreted, it is coordinate-invariant. We give the corresponding superconformal perturbation for superfield backgrounds and explain why it has no direct analog for spin-field backgrounds. We reconsider the problem of deforming a conformal field theory to a neighboring theory which is again critical. An invariant formulation of this problem is important for understanding the underlying symmetry of string theory. We give a simple derivation of A. Sen's recent formula for the change in the stress tensor and show that, when correctly interpreted, it is coordinate-invariant. We give the corresponding superconformal perturbation for superfield backgrounds and explain why it has no direct analog for spin-field backgrounds. 10/90