I will consider a perturbative expansion of the Renyi entropy, S_q, around q = 1 for a spherical entangling surface in a general CFT. Applied to conformal scalar fields in various spacetime dimensions, the results appear to conflict with the known conformal scalar Renyi entropies. On the other hand, the perturbative results agree with known Renyi entropies in a variety of other theories, including theories of free fermions and vector fields and theories with Einstein gravity duals. I will propose a resolution stemming from a careful consideration of boundary conditions near the entangling surface. This is equivalent to a proper treatment of total derivative terms in the definition of the modular Hamiltonian. As a corollary, I'll present an understanding of an outstanding puzzle in the literature regarding the Renyi entropy of N = 4 super-Yang-Mills near q = 1. A related puzzle regards the question of stationarity of the renormalized entanglement entropy (REE) across a circle for a (2+1)-dimensional massive scalar field. I will point out that the boundary contributions to the modular Hamiltonian shed light on the previously-observed non-stationarity.