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My days of algebraic manipulation are behind me  ....

I have an analysis where the planned adjustment for multiplicity was Bonferroni.
The analysis (done years ago and by someone else) used a Scheffe's adjustment.

Initially, I thought it was acceptable; "just another adjustment".
Then I thought it was perhaps an issue, as Scheffe is less conservative (although both appear to be very conservative).
Now, I am wondering if Bonferroni is perhaps a special case of Scheffe [where every pair is contrasted].

However, the days when I could take these things back to first principles are gone.  Is there anyone out there who could compare them, or simply comment?