Hi Susan. Low neutrophils has been my life for over 30 years, and enabled my CML to be diagnosed very early. My normal level was around 1.2, and I carried some broad spectrum antibiotics in case I got an infection, but rarely used them, When I moved home the new GP took a blood sample to establish a baseline. It was at the high end of normal range, and the next one was around 30, so by the time I was Dx with CML I was at 80, very much lower than most. I started on 400mg Glivec (I'm in UK) and my neutrophils fell to around 0.9. The specialist got concerned and cut my Glivec to 200 mg, but my BCR ABL wasn't making as much progress as we wanted so we went back to 400mg and I got to PCRU in about 18 months, and have remained so ever since (another 9 years or so). I am now 10 months into reducing to 200mg, still PCRU, and in September will stop taking the pills to see if I am one of the lucky 70% who can achieve TFR. My neutrophils at 200 mg are a little higher overall - I guess average of 1.1, which is progress.
So my experience says be aware but don't worry too much. Take care with hygiene, watch for horse fly bites (I changed tennis clubs to get away from one where there were too many such flies) and see how it goes.
What is you BCR-ABL number? If you have been log 4 or better for a while it would be worth discussing with your specialist whether a reduction might be possible.
Hope this helps.
Alastair