  We explore precision in a measurement process incorporating pure probe
states, unitary dynamics and complete measurements via a simple formalism. The
concept of `information complement' is introduced. It undermines measurement
precision and its minimization reveals the system properties at an optimal
point. Maximally precise measurements can exhibit independence from the true
value of the estimated parameter, but demanding this severely restricts the
type of viable probe and dynamics, including the requirement that the
Hamiltonian be block-diagonal in a basis of preferred measurements. The
curvature of the information complement near a globally optimal point provides
a new quantification of measurement stability.
