Two generalizations of the Cline-Moler-Stewart-Wilkinson "LINPACK" condition estimator are described. One generalization combines the LINPACK notion of "look-ahead" with a new feature called "look-behind" that results in a more flexibly chosen right-hand side. The other generalization is a "divide-and-conquer" scheme that involves estimating the condition of certain principal submatrices whose dimension repeatedly doubles. Both generalizations require that maximization of simple objective functions. When seeking an $L_{1}$ condition estimate, these functions are convex while inthe $L_{2}$ case they are quadratic. All the algorithms considered appear to be at least as reliable as the LINPACK estimator and are equally efficient.