  We specify sufficient conditions for the square modulus of the local
parameters of a family of GL(n) cusp forms to be bounded on average. These
conditions are global in nature and are at present satisfied for n less than or
equal to 4. As an application, we show that Rankin-Selberg L-functions on GL(m)
x GL(n), when m and n are less than or equal to 4, satisfy the standard
convexity bound.
