  We consider a tower of function fields F_0 < F_1 < ... over a finite field
such that every place of every F_i ramified in the tower and the sequence
genus(F_i)/[F_i:F_0] has a finite limit. We also construct a tower in which
every place ramifies and the sequence N_i/[F_i:F_0] has a positive limit, where
N_i is the number of degree-one places of F_i. These towers answer questions
posed by Stichtenoth.
