Abstract: Let X be a sum of real valued random variables and have a bounded mean E[X]. The generic Chernoff-Hoeffding estimate for large deviations of X is: P{X-E[X]>=a}<=min_{y>=0}exp(-y(a+E[X]))E[exp(y X)], which applies with a>=0 to random variables with very small tails. At issue is how to use this method to attain sharp and useful estimates. We present a number of Chernoff-Hoeffding bounds for sums of random variables that may have a variety of dependent relationships and that may be heterogeneously distributed.