"The result was 7.1 ug/dl, normal range 4.8-19.5. I'm not sure what he was expecting, no comment from him yet. When you talk about 'too low' cortisol levels, are you meaning low normal or out of range too low?"
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I'm glad you said "normal range" because that is what it is. On days when your stress level is lower your adrenals might only need to produce 4.8. On stressful days your adrenals may need to produce 19.5 --- even this range isn't a fixed range. Some people do fine with less cortisol and others need a lot more. Your body needs to regulate this and it is impossible for us to do this by taking Prednisone. We can only do the best that we can depending on the circumstances.

Symptoms really matter here more than a cortisol level. You have to be able to distinguish between symptoms of adrenal insufficiency/prednisone withdrawal and PMR or whatever is being treated. At one stage it was said that I had inflammatory arthritis, PMR and secondary adrenal insufficiency caused by Prednisone. Sometimes it all was lumped together and called "systemic inflammation." I would just call it one big inflammatory mess.
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"If pmr appears to be inactive but you are symptomatic, either you have prednisone withdrawal, adrenal insuffiency, or something besides pmr is causing symptoms. It's a big dilemma."
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It doesn't have to one thing as in "either PMR /or" something else. I can easily be many things combined. It is a big dilemma and something I learned late in the game. It was very surprising to everyone involved when I was able to taper off Prednisone the first time. The focus was controlling PMR and maybe large vessel vasculitis and that was what Actemra was used for.

Almost as soon as I tapered off Prednisone the first time, I had a massive flare of uveitis while I was still on Actemra. My ophthalmologist restarted 60 mg of Prednisone again and switched my biologic. My ophthalmologist insisted that I be put on Humira instead of Actemra and said Humira was "optimal" for uveitis.

Humira may work for uveitis but it didn't work for PMR. As I tried to taper off Prednisone the second time, I couldn't go any less than 15 mg because PMR returned. My rheumatologist said it would be impossible to optimally treat everything.

My endocrinologist was clamoring for me to taper off Prednisone for fear that secondary adrenal insufficiency would recur.

My ophthalmologist wanted me to stay on Humira.

In the end ... we all had our say. However, I had the final say because my rheumatologist gave me the choice. I choose Actemra much to the chagrin of my ophthalmologist.

My endocrinologist was eventually happy. I was able to taper off Prednisone incredibly fast the second time after Actemra was restarted. This was even after being on Prednisone another year after I tapered off the first time. All my endocrinologist could say was that I had resilient adrenal glands and I was extremely lucky.

Just checking, can't you use a combination of 2.5 mg and 1 mg prednisone pills to taper by .5 mg?
A 2.5 and 2 1s would give you 4.5. I apologize if I'm missing something.

"Is tapering in whole mg amounts immunologically safer/as safe as tapering half mg amounts?"
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I personally don't think tapering by half mg amounts is necessary. I tried that too and it didn't make any difference. I agree with @jeff97 and just request the 2.5 mg and 1 mg tablets. Using those two tablets should allow you to do .5 mg increments except for 1.5 mg and .5 mg.

I have done it the way your rheumatolgist suggests too by doing 5 mg one day and 4 mg the next. Over 2 days, that averages 4.5 mg. That makes more sense to me if you want to prompt your adrenals to produce cortisol again. On the day you take the 4 mg dose that might give your adrenals a hint to make up the difference and produce some cortisol. I'm not sure if it works that way or not. I mostly say whatever works for you is all that matters.

I was flabbergasted when my endocrinolgist told me there was no need to taper from 3 mg to zero IF my cortisol level was adequate. It depended more on my cortisol level than my autoimmune disorders.

I think my endocrinologist consulted with my rheumatolgist to make sure I didn't need Prednisone to treat PMR. She also asked me I thought I needed Prednisone for PMR. I wasn't sure but Actemra seemed to have PMR under control.

Actemra wasn't intended to prevent uveitis from recurring. However, after some dose adjustments made easier with an infusion, of Actemra, it now seems like it can prevent flares of uveitis too.