  The penalty incurred by imposing a finite delay constraint in lossless source
coding of a memoryless source is investigated. It is well known that for the
so-called block-to-variable and variable-to-variable codes, the redundancy
decays at best polynomially with the delay, where in this case the delay is
identified with the source block length or maximal source phrase length,
respectively. In stark contrast, it is shown that for sequential codes (e.g., a
delay-limited arithmetic code) the redundancy can be made to decay
exponentially with the delay constraint. The corresponding redundancy-delay
exponent is shown to be at least as good as the R\'enyi entropy of order 2 of
the source, but (for almost all sources) not better than a quantity depending
on the minimal source symbol probability and the alphabet size.
