  We show that a reddening sequence exists for any quiver which is Banff. Our
proof is combinatorial and relies on the triangular extension construction for
quivers. The other facts needed are that the existence of a reddening sequence
is mutation invariant and passes to induced subquivers. Banff quivers define
locally acyclic cluster algebras which are known to coincide with their upper
cluster algebras.The existence of reddening sequences for these quivers is
consistent with a conjectural relationship between the existence of a reddening
sequence and a cluster algebra's equality with its upper cluster algebra.Our
result completes a verification of the conjecture for Banff quivers. We also
prove that a certain subclass of quivers within the class $\mathcal{P}$ define
locally acyclic cluster algebras.
