  We revisit the Karagiannidis-Lioumpas (KL) approximation of the Q-function by
optimizing its coefficients in terms of absolute error, relative error and
total error. For minimizing the maximum absolute/relative error, we describe
the targeted uniform error functions by sets of nonlinear equations so that the
optimized coefficients are the solutions thereof. The total error is minimized
with numerical search. We also introduce an extra coefficient in the KL
approximation to achieve significantly tighter absolute and total error at the
expense of unbounded relative error. Furthermore, we extend the KL expression
to lower and upper bounds with optimized coefficients that minimize the error
measures in the same way as for the approximations.
