The no-load voltage will stay nearly 3.6 volts well into discharge. I have an 11-year-old Tadiran TL-5151 battery that just showed 3.69 volts open-circuit on my Fluke 189 DMM (a really nice unit, BTW, that has given wonderful service). Put a 75-ohm resistor across that battery and the voltage drops to under 0.7 volts.
A brand-new SAFT or Tadiran will drop to about 3.35 volts with that 75-ohm resistor across it, which corresponds to a load current of about 45 ma. The Thevenin equivalent internal resistance (or Norton for those of a current mind) in the good battery is on the order of 6-7 ohms, as opposed to three or four hundred for the very old, discharged battery (which was probably shipped with my B&W G3, judging by the date). That is why the battery I describe has three letters put on it in magic marker.
So, the point is that *open-circuit voltage readings are not helpful*, especially with older batteries that have been in a machine for a while.
I also have a "May-03" Tadiran that is similarly magic marked, which kind of suggests that I placed it in the G3 at about four years. That's seven years ago, so I don't remember if I had problems or just replaced it preemptively.