This paper presents a novel Kalman-filter-based approach for approximately enforcing a linear constraint in adaptive control. One application is that this leads to alternative forms for well-known modification terms such as e modification. It is shown that employing this approach does not increase the theoretical guaranteed ultimate bounds for the closed-loop error signals of an existing adaptive design. In addition, it leads to smaller tracking errors without incurring significant oscillations in the system response and without requiring high modification gain. Three novel modifications to classical adaptive laws are illustrated and tested on a model of wing rock dynamics.