Feature terms are a generalization of first-order terms which have recently received increased attention for their usefulness in structured machine learning, natural language processing and other artificial intelligence applications. One of the main obstacles for their wide usage is that, when set-valued features are allowed, their basic operations (subsumption, unification, and antiunification) have a very high computational cost. We present a Constraint Programming formulation of these operations, which in some cases provides orders of magnitude speed-ups with respect to the standard approaches. In addition, exploiting several symmetries – that often appear in feature terms databases – causes substantial additional savings. We provide experimental results of the benefits of this approach.