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You probably have been told to disregard anything under 7cM because it may be a false positive. Then again you may be depriving yourself of and entire line on your tree. My father's line was German/Polish and Russian and he knew nothing of his line. I was only able to trace his father to Marianow, Russia and eventually found out about his father (my g-grandfather, abt 1860's). I and many family members did dna testing probably 3 yrs ago now and it amazed me but most of my matches were on my paternal line. Fortunately, I have been doing my own genealogy for over 35 years and have substantial documentation. I ended up having one match >8cM's and on the same segment, multiple 3-5cM matches. It seems that the 3cM matches had extremely good documentation and 1 couple matched her tree and was then able to help me get back to the early 1700's and sometimes earlier. The stories they were able to tell me were troubling but fantastic about the hardships their families and ultimately my ancestors had to bear. Most of my matches actually are at smaller levels (apparently since where I match is back > then the 6th generation) and if I can ever find out how to utilize the x chromosome, my mtdna and my cousins y-dna it should open a wealth of information. Good luck to everyone!
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False matches
Most matches of 3 cM are still false, even if you find shared ancestors.
If you and the other person were each able to test both parents you would find that the majority of 3 cM segments shared by between you and the other person were not inherited from your parents: they're just an artefact of the DNA analysis which can't distinguish between maternal and paternal DNA.
A few small segments would survive that process i.e. you'd find that the same segment was also shared by one of your parents and one of the other person's parents. You might even find that both of your parents have that segment, which immediately flags it up as being a segment which is just very common and not likely to indicate a relationship in a genealogical timeframe.
Even if you assume that small segments are real, they're generally not a reliable indicator of a relationship. I've tested to of my siblings as well as myself. Three known cousins, who are each other's siblings, have also been tested. When you test three or more siblings it's possible to work out which segments of DNA were inherited from which of the four grandparents and create a "chromosome map". I've done this for my family and for my cousins.
The cousins and I are related via our respective paternal grandfathers (their grandfather was my great-grandfather's brother).
Comparing myself to one of these cousins, checking small segments against our "chromosome maps", I can see that the majority of segments are on parts of chromosomes where one or both of us did not inherit DNA from our paternal grandfathers. That means that the majority can't be in any way related to the known shared ancestry. They are either totally false matches, or they indicate multiple lines of very distant relationships which we don't know about.
Taking the few remaining small segments which fall in areas where my cousin and I do both have DNA from our paternal grandfathers:
a) If I had the inclination to research more thoroughly by comparing my siblings and the other two cousins, some would be proved to be totally false matches. Many others would turn out not to be from the paternal grandfathers (just because the cousin and I both have our paternal grandfathers' DNA at that point doesn't mean that the shared segment isn't from our maternal DNA).
b) My map is limited to my grandparents' level. Anywhere I have my paternal grandfather's DNA, there's a 50:50 chance of it being his mother's DNA which is not my link to my cousin.
Similarly, my cousin's map is limited to her grandparents' level. Anything marked as coming from her paternal grandfather could be from either one of his parents (my great-great-grandparents). If my grandfather did pass on his father's DNA rather than his mother's, it could be from either one of my great-grandfather's parents, with a 50:50 chance of it being the opposite shared ancestor. So, even if my cousin and do I both have DNA from our respective paternal grandfathers (who were our link to each other) there's a high chance that the DNA didn't come from the same ancestor and any shared segment is either false or coincidental.
Over all, out of thirty seven segments of 3-7 cM which I apparently share with this cousin, just one (4.9 cM) has been confirmed.
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