  We present precision corrections to dispersion relation bounds on form
factors in bottom hadron semileptonic decays and analyze their effects on
parameterizations derived from these bounds. We incorporate QCD two-loop and
nonperturbative corrections to the two-point correlator, consider form factors
whose contribution to decay rates is suppressed by lepton mass, and implement
more realistic estimates of truncation errors associated with the
parameterizations. We include higher resonances in the hadronic sum that,
together with heavy quark symmetry relations near zero recoil, further tighten
the sum rule bounds. Utilizing all these improvements, we show that each of the
six form factors in B --> D l nu and B --> D^* l nu can be described with 3% or
smaller precision using only the overall normalization and one unknown
parameter. A similar one-coefficient parameterization of one of the Lambda_b
--> Lambda_c l nu form factors, together with heavy quark symmetry relations
valid to order 1/m^2, describes the differential baryon decay rate in terms of
one unknown parameter and the phenomenologically interesting quantity (\bar
Lambda)_Lambda \approx M_{Lambda_b} - m_b. We discuss the validity of
slope-curvature relations derived by Caprini and Neubert, and present weaker,
corrected relations. Finally, we present sample fits of current experimental B
--> D^*l nu and B --> D l nu data to the improved one-parameter expansion.
