Using simple, intuitive arguments, we discuss the expected accuracy with which astrophysical parameters can be extracted from an observed gravitational wave signal. The observation of a chirplike signal in the data allows for measurement of the component masses and aligned spins, while measurement in three or more detectors enables good localization. The ability to measure additional features in the observed signal—the existence or absence of power in (i) the second gravitational wave polarization, (ii) higher gravitational wave multipoles or (iii) spin-induced orbital precession—provide new information which can be used to significantly improve the accuracy of parameter measurement. We introduce the simple-pe algorithm which uses these methods to generate rapid parameter estimation results for binary mergers. We present results from a set of simulations, to illustrate the method, and compare results from simple-pe with measurements from full parameter estimation routines. The simple-pe routine is able to provide initial parameter estimates in a matter of CPU minutes, which could be used in real-time alerts and also as input to significantly accelerate detailed parameter estimation routines.