Hi Clelia,
  I remember my sister (who was 20 years older than I am) making batches
and batches of jam with no sugar at all, but I can't remember how she did it.

If the berries are sweet enough, that could probably be done.
It is so cloudy here lately that the berries are not as sweet as they could
be...
Here is what the very unpaleo skies look like at my place:
http://www.rense.com/politics6/chemdatapage.html

Paleobest,
Susan