Looking for encoder with 16 detents

[nebula]

I am trying to find encoders with exactly 16 detents per revolution for a good price.  I ordered an encoder from Digi-Key (Panasonic # EVE-QDBRL416B , digi-key # P12423-ND), which is "16 pulses per revolution", but I didn't realize that this actually means 32 detents.

Does anybody have a suggestion as to where to look for an inexpensive 16-detent encoder?  The weird thing is that the one I got is only a few bucks from Digi-Key, and the ones that actually have 16 detents cost about 4 times as much.  I'm looking for 2-10 pieces, and I don't want to spend 10 bucks each.  Integrated pushbutton switch is optional.

Thanks