(joint work with Vern Paulsen, Mrinal Raghupathi and Dinesh Singh) We consider NevanlinnaPick interpolation on the unit disk with the additional constraint that the bounded analytic functions satisfy f′(0) = 0. We obtain necessary and sufficient conditions for scalar interpolation by a function of norm 1 in terms of a family of Pick conditions associated to a natural family of reproducing kernel Hilbert spaces. An analysis of C*-envelopes is used to show that these same conditions do not suffice for matrix interpolation.