  This paper presents prefix codes which minimize various criteria constructed
as a convex combination of maximum codeword length and average codeword length
or maximum redundancy and average redundancy, including a convex combination of
the average of an exponential function of the codeword length and the average
redundancy. This framework encompasses as a special case several criteria
previously investigated in the literature, while relations to universal coding
is discussed. The coding algorithm derived is parametric resulting in
re-adjusting the initial source probabilities via a weighted probability vector
according to a merging rule. The level of desirable merging has implication in
applications where the maximum codeword length is bounded.
