For years (decades!), every time I went to my dentist, he would stress daily flossing and massaging my gums with stimudent. Brushed daily, but rarely flossed. (One roll of floss would last for a year!) I was a bleeder. Look at my gums and they would bleed. Fortunately, the my pockets were mosts 2's and 3's, maybe a few 4's. I was told that brushing and flossing was most effective on pockets 3mm or less. After that, a dentist or perio may have to treat them.
Recently, for some unknown reason, I started to brush(ultarsonic)and FLOSS after EVERY meal or snack. Within a week most of the bleeding stopped. After less than a month, no more bleeding, not even a trace of a pink in the sink. Dentist is amazed at how health my gums are, though not surprised at the results. No matter where he poked, result was the same: No blood! The gums had tightened up and the depth of pockets reduced.
If only I had started this relationship with floss when I was young!
I agree with Forum-DDS-JB. You should be able to maintain the pocket and possibly eliminate it with good home care and regular professional care. If the pocket increses to 5 mm then have the dentist treat it. I have seen many 4 mm pockets resolved with good home care and regular prophylaxis. The biggest challlenge the profession has is patient compliance.
I am not sure that the pockets that are 4mm. can be eliminated but I think they are maintainable.I certainly would not like to see them get any deeper.Your age comes into play here. The younger you are the more aggressive I would be to try to eliminate these pockets.Your perio condition should be closely monitored.