Robots are finding new applications where physical interaction with a human is necessary, such as manufacturing, healthcare, and social tasks. Accordingly, the field of physical human–robot interaction (pHRI) has leveraged impedance control approaches, which support compliant interactions between human and robot. However, a limitation of traditional impedance control is that—despite provisions for the human to modify the robot’s current trajectory—the human cannot affect the robot’s future desired trajectory through pHRI. In this paper, we present an algorithm for physically interactive trajectory deformations which, when combined with impedance control, allows the human to modulate both the actual and desired trajectories of the robot. Unlike related works, our method explicitly deforms the future desired trajectory based on forces applied during pHRI, but does not require constant human guidance. We present our approach and verify that this method is compatible with traditional impedance control. Next, we use constrained optimization to derive the deformation shape. Finally, we describe an algorithm for real-time implementation, and perform simulations to test the arbitration parameters. Experimental results demonstrate reduction in the human’s effort and improvement in the movement quality when compared to pHRI with impedance control alone.