"My doctor disagrees with this and thinks I need to keep trying but she has no advice on how to do this. All very frustrating!"
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I know this feeling well. I was in the same predicament about 6 years ago.

It was very frustrating to me too when I was still on 10 mg of Prednisone after 12 years of PMR. I was "comfortable" on 10 mg of prednisone but my PMR symptoms would start to return if I tapered down to 7 mg. The dead slow method didn't work for me either except the inevitable flare was somewhat delayed. If I continued to taper down to 3 mg, I would always flare. I would do the same as you and go back to 10 mg and try again.

My rheumatologist also wanted me to keep trying to taper off prednisone until I said I wasn't going to try anymore. I wasn't giving up but I insisted on something else besides Prednisone to control my symptoms. I was at a standstill until my rheumatologist suggested something as a "last resort" because "taking prednisone for the rest of my life wasn't a good outcome."

The last resort was a biologic that controlled my PMR symptoms while I tapered my prednisone dose lower. I didn't experience any PMR symptoms at 7 mg when I took the biologic. I tapered by 1 mg per month from 10 mg to 7 mg. I decided to get the inevitable flare over with so I tapered by 1 mg per week for the next 4 weeks down to 3 mg.

I was stuck on 3 mg but not because of PMR symptoms. I was uncomfortable tapering any lower than 3 mg because I didn't feel well and I was having dizzy spells. I told my rheumatologist who checked my cortisol level and it was low so I was referred to an endocrinologist.

The endocrinologist didn't want me to taper any lower than 3 mg because my cortisol level was too low. She wanted me to stay on 3 mg for as long as it took for my cortisol level to improve. After 6 months my cortisol level improved enough that the endocrinologist said I could try to stop prednisone. She said as long as my cortisol level was "adequate" there was no need to taper from 3 mg because it was a low dose. She said I could go from 3 mg to zero without tapering but I should "take prednisone again for any reason if I felt the need." With that reassurance I stopped prednisone and I basically went from 3 mg to zero in a couple of days.

I had a need to take 60 mg of Prednisone again but only temporarily. I was off Prednisone again 6 months later after some adjustments were done to my biologic dose.

I have now been completely off prednisone for the past 3 years