Summary: The quasi-steady-state assumption (QSSA) of biochemistry is studied as an approximation that is important in itself and also that exemplifies an approach to ODE systems with an initial fast transient. Simple estimates of the two relevant time scales of the underlying problem are made. These estimates lead to a dimensionless formulation containing a different small parameter from that which is customary. Earlier results on the QSSA are surveyed in the context of the new nondimensionalization. It is shown that more comprehensive and simpler error estimates can now be made. Some general methodological hints are drawn from this example.